The term bun fight is evidently widely used across nations of the old British Commonwealth and goes back to the late 1800s.
'Bun fight' in slang dictionaries
The traditional meaning of bun fight appears in a glossary entry in Hippocrene Language and Travel Guide to Britain (1996):
tea fight or bun fight — tea party
Jonathon Green, The Dictionary of Contemporary Slang (1984) offers a bit of a twist on that definition:
bunfight n. a tea party, esp. with image of children struggling for sticky buns.
This suggests a fight over buns rather than with buns.
Ann Barr & Peter York, The Official Sloane Ranger Handbook: The First Guide to What Really Matters in Life (1982) explicitly takes issue with the Oxford English Dictionary with regard to the term's meaning, though why we should believe Barr & York is not entirely clear:
bun-fight n. Crowded party where you have to fight to get something to eat. (The Oxford Dictionary errs in supposing bun-fight means tea-party.)
Norman Schur, British English A to Zed: A Definitive Guide to the Queen's English (2013) takes a more demure line:
bun fight, n. approx. very large tea party Inf[ormal] Sometimes bun feast. There is no equivalent jocular American colloquialism. Can also apply to a cocktail party or similar get-together.
Eric Partridge manages to multiply the difficulty by finding ten additional terms to grapple with. First from Partridge, Dictionary of Slang and Unconventional English, second edition (1938):
bun-feast or -fight. A tea party : late C. 19–20 coll[oquial] Cf. crumpet-scramble ["A tea-party : from ca. 1860 : coll[oquial] Derby Day, 1864, 'There are men who do not disdain muffin-worries and crumpet-scrambles.'"], muffin-worry ["muffin-fight ; muffin-worry. A tea-party : coll[oquial] resp[ectively] ca. 1885–1910 and 1860 H., 2nd ed. (also in Ouida, 1877). O.E.D."]"].
his edition of Partridge also has an entry for bun-struggle or bun-worry:
bun-struggle or -worry. A tea-party for sailors or soldiers : military and naval : from ca. 1870. In C. 20 the struggle form is ob[solete]. Cf. tea-fight ["A tea-party : 1849. Albert Smith (O.E.D.): s. ca. 1880, coll[oquial]. Occ[asionally] tea-scramble (C.20 : Manchon) and tea-shine "].
And then from Partridge, Dictionary of Slang and Unconventional English, eighth edition (1984):
bun-beat or -fight. A tea-party: late C.19–early 20 coll[oquial].
So that brings the jocular variants on a tea-party theme to a crooked baker's dozen (bun-beat, bun-feast, bun-fight, bun-struggle, bun-worry, crumpet-scramble, muffin-fight, muffin-worry, tea-fight, tea-scramble, and tea-shine).
'Bun fight' in the wild
Limiting the inquiry to the bun-based terms, I find these early specimens. From William Black, Wild Eelin: Her Escapades, Adventures & Bitter Sorrows (1898):
Miss Eelin, I can see you on the first floor of the Old Ship, looking out. Oh, I know the place; trust me; you trust me: if I can't order a ripping little lunch for the two of us, then take me away and fling me into the nearest horse-pond. And you're coming to the ball tonight. Yes, you are. Your mother's sure to be better by then. I'll be waiting for you—now mind. All the barn-doors; and we'll sit out the lancers—and the waltzes, too, if you like; and we'll make it a perpetual bun-fight for old Mother Helmsdale. ...
From "Temperance at Shahjehanpur," in The Thin Red Line: The Regimental Paper of the 2d Batt., (Princess Louise's) Argyll & Sutherland Highlanders (April 1899):
Previous to this there had been a "bun-fight" with an enormous casualty roll, and afterwards there was a concert in which several friends of the Royal West Kent Detachment figured conspicuously.
From Lilian Quiller-Couch, "The Love Affairs of Patricia—I Try to Amuse Cousin George" in The Saturday Evening Post, volume 174 (1901):
A ray of understanding crossed Cousin George's face.
"I'm not going to that blessed old Sunday-school bun-fight," he declared decidedly.
"It is to be deplored," I remarked to the sky, "when the educated classes sink into vulgarity of expression."
From "The Library Press" in The Library World: A Medium of Intercommunication for Libraries (February 1902):
The Library Assistant for January contains a portrait of Mr. A. Cotgreave, reports of various meetings and of the fourth annual bun fight, a short article on " How to Popularise a Public Library," by Mr. W. J. Harris, and interesting notes and news.
From "Stray Shots from Solomon," in The Canadian Shoe and Leather Journal (May 1905):
SHAMBLING TO THE SHAMBLES.—There go two fellows towards the corner, the first marches ahead with a swagger and stride like that of a hero; the second follows two paces in the rear with a sheepish look that betokens the realization that the "fatted calf" is about to be killed on his behalf. The bustling energy of the first is apt to lead you to the conviction that there is some important business on hand, while the slinking gait of the second, would make him a dead easy winner in a natural modesty contest at a Sunday School bun fight.
'Bun fight' as trouble
When bun fight came to mean (figuratively) a spat, dispute, or other conflict is difficult to identify with specificity, but it certainly had that meaning in "Bun Fight Over a Sex Book," in the [Sydney, New South Wales] Bulletin (1980) [combined snippets]:
An extraordinary bun fight has broken out in New York's precious literary world over Gay Talese's book on American sexual mores, Thy Neighbor's Wife. Critics have panned it with unusual ferocity and Talese has hit back with even more venom. Philip Mobile reports on Page 66.
From Australian Government Publishing Service, Proceedings of the Conference, volume 1 (1982) [combined snippets]:
MR SCHMIDT (General Manager - Inbound, Thomas Cook) - Probably I will be labouring an old subject. The idea of parochialism is only good if it does not create a 'bun fight'. Regrettably, especially amongst the State tourist bureaux overseas, the approach appears to be not: 'Let us work together' but rather: 'I will promote my little section'. There has developed a 'bun fight' that is not only obvious to the people here but also to the industry overseas. In that respect parochialism is bad. It is bad unless people are promoting together rather than individually. I would much prefer a lot of these people, especially State tourist bureaux, to use their money to get their people on the right track.
And from Northern Ireland Assembly, Official Report of Debates, issue 4 (1982):
Mr Edgar Graham: I promise not to delay the House very much longer in this matter because the matter has already been discussed up and down on the Second Reading debate as it were an on this Committee Stage debate. A number of matters of law have been raised by hon Members, and although in the Procedure Committee we have a quare old legal bun-fight already and I think we are going to have perhaps a good legal bun-fight here over this Standing Order there may well be a quare old legal bun-fight after these proceedings over this. I think that since the hon Member for East Belfast (Mr Napier) has raised the ghost or prospect of a High Court action over this, the House should be aware of what may be an anomaly in the legislation establishing this Assembly in that although, as the hon Member for North Belfast (Mr Maguire) has said, we are a creature of statute, the privileges and immunities of the House of Commons extend to this Assembly.
None of these later instances seem to be referring to tea parties—at least not pleasant ones. But almost certainly the later meaning derives from the earlier "tea-party" meaning, and seems to entail a social gathering gone wrong.
The sense of "bun fight" as a specifically legal or procedural tiff finds support in Export Today, volume 11 (1995) [combined snippets]:
In what has been dubbed "a sizzling bun fight," the U.S. hamburger chain McDonald's is appealing a South African court decision in a trademark infringement fight with a local company that is using the McDonald's name.
In October, a Pretoria court ruled against McDonald's, saying the U.S. company abandoned its trademark by not opening any restaurants during the apartheid era. The court awarded the trademark to the local operator, who had been using the name in recent years.
From Aboriginal Law Journal (1995) [combined snippets]:
It becomes apparent from the forced changes in colonial policy that the colonial powers were at their wit's end about what to do with the Aborigines. It was a despairing colonial administration, Reynolds points out, which sought the services of George Augustus Robertson, who in turn made promises to the Aborigines. Hence, Reynolds points out, the petition represented more than a bun-fight between white overseers - it referred to a broken promise on matters of substance.
And from Barbara Farbey, David Targett & Frank Land, Hard Money, Soft Outcomes: Evaluating and Managing the IT Investment (1995):
And worse still when we invoked penalty clauses, the section in the contract that talked about the penalty clauses was so ambiguously written that we had a bun fight for nearly 6 months over it. It wasn't the question of how much (it turned out to be something like 30,000, which over a multi-million contract was pretty small) but it was the bun fight that was the problem, the fact that they (the vendor) didn't just walk in on the following Monday and say 'we screwed up last week, we were down for three days, and according to the contract this is what you are owed'.
Later instances of the term suggest that conflicts may be distinguishable into "legal bun fights" and "political bun fights." But whatever the antagonistic possibilities of bun fight in its modern slang senses, the traditional slang sense persists as well. From Rhys Bowen, A Royal Pain (2008):
"Darling what a lovely surprise. I had no idea you'd be part of this bun fight.”
“Belinda, what are you doing here?” I asked.
“Darling, have you ever known me to turn down a free meal? I told you I was going to the country. One simply can't stay in London when the weather turns warm.”
A bun fight can mean simply a tea party—as it has for more than a century. Or (in more-recent decades) it can mean a dispute over social proprieties, legal rights, or political power. One common characteristic of these various meanings is the suggestion that the gathering goes on rather longer than the participants might wish.
The earliest of the bun-related terms for tea party may be bun-worry; at any rate it is the earliest such term to appear in a Google Books search. From "Sketches of Irish Life," in Once a Week (November 16, 1872, and December 7, 1872):
I had gone into the country for a day's shooting, and also for the purpose of gracing with my presence a soiree of bun-worry which was to come off at a school-room not far from my friend's house.
"Boys," said the latter gentleman, as he pushed his last empty cup from him with a satisfied air—"boys, it stracks me we'll make a scatterment among the victuals at the bun-worry the night."
"I think it," was Bill's sage reply.
Unquestionably, people invited to tea have been worrying, feasting, struggling, beating, and fighting with buns for a very long time.