I have a colleague of whom this is a favorite phrase, used in the sense of "knock yourself out", "go for it", "have at it", "go to town", "help yourself". ("You want to add that feature to the software? Go ahead - fill your boots!")
So far, the best origin story I've heard is that of "when plundering, using every available container - i.e., even your boots". It feels as though there may be more to it than this, but I've not discovered it yet. What say?
A quick search yielded
At the HMS Victory museum in Portsmouth UK, you can buy a thick leather cup lined with pitch. This is a replica of the sailor's mug used on board in Nelson's time, and it was used (among other things) for the rum ration when issued. This cup is called a "boot", and when things were good and you got an extra rum ration, sailors were told "Fill Yer Boots"!
As all good sayings do, it comes from a sailor.
The following is an excerpt from Memoirs of Serjeant Paul Swanston: being a narrative of a soldier's life, in barracks, ships, camps, battles, and captivity on sea and land; with notices of the most adventurous of his comrades. (no, that's really the full name of the book), first published in 1818.
In quick time they were at the wine-pipe; for a moment the new hands seemed at a loss for the means of getting the wine to their mouths; but the "wide-a-awake" boy sliped (sic) off one of his shoes in a twinkling, dipped it into the cask and drank.
"Drink, you devils, drink!" he said; "its all one how much you drink, only don't get drunk!" And again he filled his shoe, and again he drank. The previous debauch in connexion with the new, soon tumbled him on the ground; and he lay there gradually sinking into stupidity; but, as he took his leave of consciousness, he admonished the others to take care of themselves; to take as much as they could rightly carry; but not to get drunk, saying, as he sunk lower and lower himself, "Fill your boots, boys—fill your boots! Give me one small drop in a shoe to make me well again, for I'm— I'm—."
Alas, poor humanity! There lay in the deepest degradation, as good a fighting soldier, and, when he could not get drink, as cleanly and active a fellow as ever the English army possessed.
I can't think of anything more exemplary of gusto than a sailor getting blind stinking drunk out of his shoe.
You can read the full text here.
It appears to have naval origins, but the evidence is still only 20th century (1948) and there's no suggestion of it originating from dipping a special boot/cup into rum in Nelson's time, but rather being able to eat so much until your boots are also full.
The OED says it's a British colloquial phrase meaning:
to take full advantage of an opportunity to benefit oneself; to take as much as one wants of something.
The earliest quotation in the OED is relatively recent:
1969 J. Burmeister Hot & Copper Sky iv. 67 I'll bet you're filling your boots.
It appears in snippets of a 1950 navy slang dictionary, Sea slang of the twentieth century: Royal Navy, Merchant Navy, yachtsmen, fishermen, bargemen, canalmen, miscellaneous by Wilfred Granville:
Big eats — fill your boots ! The lower-deck invitation to any meal. Cf. LUVERLY GRUB; DIG IN, FILL YOUR BOOTS !
Dig in — fill your boots ! The mess-deck cry when dinner is served.
Dictionary of Catch Phrases by Eric Partridge (1992) offers an explanation:
dig in and fill your boots; often and is omitted. Eary hearty!: fill not only your belly but, if you wish, your boots as well: RN: C20. (PGR, 1948.) Cf eat up ... and muck in ...
RN is Royal Navy; C20 is 20th century; PGR is a reference to a book by the same Partridge and Granville:
PGR is E. Partridge, W. Granville and F. Roberts, A Dictionary of Forces' Slang: 1939 - 45, 1948
I grew up in rural Yorkshire after the second world war and the expression fill your boots referred to an involuntary bowel movement caused by great fear, for example, being chased by a bull, or some equally terrifying event.
Fill your boots was a polite way of saying one had "S… oneself". When you consider people wore wellington boots with their trousers tucked in it is easy to understand the meaning of the phrase.
Only in recent years have I heard the expression used in different contexts, mostly with a positive inflection. I asked a Canadian friend, born and bred in a farming community, if she was familiar with the phrase. Yes, it's the involuntary consequence of being chased by a bull— though she didn't put it quite like that!
English coal miners wore hobnailed boots which were slippery on cobblestone streets, so they carried them home after work so they wouldn't slip. This allowed them to "fill their boots" with coal which would be just enough coal for a family for one day. Considered one of the perks of working in a coal mine.
I came across this phrase in the book "Or I'll Dress You in Mourning," which came out in the 60's about the most celebrated Matador who has ever lived. The phrase was explained thus.
"Fill your boots!" is a phrase matadors use to wish there fellow matadors good luck in the ring. It is similar to the theatrical phrase "break a leg" however the "fill your boots" phrase suggests that the matador heading into the ring fills his boot with blood from being gored.
In Nova Scotia, it is said that a fisherman's catch was so good that when he ran out of crates, he filled his boots with fish to get them on the wharf.
I believe this could originate with 'The Tinder-Box' by Hans Christian Anderson (1835), where the soldier fills not only his pockets, but his cap and boots with gold. Hence 'fill your boots'.
Urban Dictionary has an entry dating from 2005:
http://www.urbandictionary.com/define.php?term=fill%20your%20boots
Google reveals a number of references to the phrase, including a punk rock album title. I can't find any definitive reference, but the explanations seem to center around the Cavaliers, boots, and the usual horse-hockey you find in etymology.
I think the common-sense explanation you've arrived at is probably the right one.
I've been told that in ancient sea fairing days, ships officers were traditionally not allowed the leave the captains tables before the captain did for fear they would talk of mutiny between the crew. So if a officer needed too relieve himself during the meal he was orders to "fill yer boots"
My understanding is that there was a theft investigation after firemen put out a small fire in a store. The investigation revealed that the firemen had filled their high rubber boots with small items stolen from the store.
"Fill your boots" was an order given by William of Orange to his troops before the Battle of the Boyne. The boots refered to leather water carriers that each soldier had strapped to his saddle.
