Nigel Rees, A Word in Your Shell-like: 6,000 Curious and Everyday Phrases Explained (2004) has this relevant entry:
sod this for a game of soldiers (or beggar this ... or blow that ... or fuck this ...) Expression signifying that one is giving up some activity through exhaustion or disillusionment. 'Beggar' is, of course, a soft form of 'bugger', but quite what is meant by a game of soldiers in either version of the expression is not totally clear. Perhaps the speaker considers the activity being abandoned as pointless as a game of toy soldiers or as futile as the 'army game' (life as a professional). Compare FUCK THIS (OR THAT) FOR A LARK! [The entry for this term reads "Expression of disgust at some chore or duty imposed. Mostly British use since the 1940s. Laurence Olivier is said to have used a cod French translation: 'Baisez cela pour une alouette.'"] Perhaps none of these date from before the Second World War. 'I met him in the pub one summer. I'd just been stood up by a man I was having a relationship with. Blow that for a game of soldiers, I thought, when suddenly Jim appeared from one corner of the pub and offered me a drink' – Independent on Sunday (13 February 1994).
Eric Partridge & Paul Beale, A Dictionary of Slang and Unconventional English, eighth edition (1984) notes that 'skittle' sometimes replaces 'soldiers' in variants of the expression:
fuck that (or this) for a game of skittles (or soldiers)! and fuck that (or this) for a lark! Elaborations of fuck that!, an emphatic condemnation of any activity in which one is , or could be, forced to join. the exclam[ation] being often ruefully joc[ular], since there is no help for this situation. Soldiers is an army var[iant] of C.20; skittles, which often implies underhand cunning, also C.20; lark, since latish C.19. The shortest, the orig[inal] and basic, prob[ably] throughout C.19–20, is as so often, the strongest; orig[inally] very low.
I didn't have any luck finding early pre-1970 instances of "[blank] this for a game of skittles," but Google Books searches turned up several seemingly on-point instances of "[blank] this for a game of soldiers." Not surprisingly, the earliest instances appeared in military contexts.
James Landon Hodson, Through the Dark Night: Being Some Account of a War Correspondent's Journeys, Meetings and What Was Said to Him, in France, Britain, and Flanders During 1939–1940 (1941) [combined snippets]:
I met a man today who lives near a spot where air battles frequently occur. On his wireless he can hear warnings and messages called by radio from one pilot to another. The Germans shout, "Achtung! Achtung! Spitfieren! Spitfieren!" He heard a British pilot shout to another, "Keep out, don't be nosey!" He wanted that fight to himself. In the middle of a very hot mixed-up fight one of our men remarked drily on his radio, "What price this for a game of soldiers!"
From Hashomer Hatzair in Great Britain, Forging the Link: A Handbook of Hashomer Hatzair 1952 [snippet view]:
A cold gust of wind fans your face, you shiver slightly, you have been standing still, "get moving," you say to yourself, only another hour to do, the rifle is heavy, brrrr, blow this for a game of soldiers, they have no consideration at all.
From Willis Hall, The Long and the Short and the Tall: And Each His Own Wilderness, in The New English Dramatists, volume 3 (1961)[combined snippets]:
BAMFORTH: It's a crumb patrol. It's just about the crummiest detail in the Far East is this, and no messing. Two days humping kit and two days back! Routine Patrol! You can stick this for a game of soldiers. Talk about the P.B.I. If ever there was an all-time crumb patrol, we're on it. {He glances round at WHITAKER, who has taken a needle, ball of wool, and a pair of socks from his pack and is busily engaged in darning.} What the hell are you supposed to be doing?
From Charles Wood, Cockade, in Plays and Players volume 11 (1963):
DICKIE BIRD: And I could. No – to be strictly factual there's only on thing I'm sweating on ...
Harry: You're sweating on him stopping ...
GARIBALDI: Get some in.
DICKIE BIRD: And that for a game of soldiers – I'd be back in that box with the instructions 'fore you can say F.F.I.
GARIBALDI: That's your sweat.
DICKIE BIRD: Don't come to me Jack. I'll be too busy sorting out rations.
And from Stanley Middleton, Terms of Reference (1966):
'You start the ball rolling,' Jake said.
'Damn that for a game of soldiers. You're the one ...'
'No,' Jake said. 'Say something to me. Rude or otherwise.'
'D'you know,' Robert said, 'I can't think of a ... Get stuffed. That do?'
The implication in these early instances seems to be that if the real-life military situation that the soldiers are talking about in each of these instances were a game of pretend warfare and they were children playing it, they would quit in disgust or annoyance. The tone of rueful jocularity mentioned in the description by Partridge & Beale seems very much in line with the tone of phrase's usage in the examples cited above.
The earliest four examples I have cited clearly take place in a military milieu; however, I can't tell what the setting is for the conversation in Middleton's novel. In any event, "[blank] this for a game of soldiers" was in use in nonmilitary contexts no later than the early 1970s.