Im not sure how this would happen, this is my first WI, but right now, i'm considering it would happen if we had enforced the treaty of versailles, and gone to war when Hitler reoccupied the Rhineland in 1936, even though public opinion was against this.
That's not a likley place to do it. Both the Rhineland and Austria (and the re-armament "revalations") were fait accomplis: we thought the status-quo was unsustainable, we wanted to change it as part of an imaginary "general settlement of German grievances", and they figured we wouldn't mind much if they just took it.
Czechoslovakia is the place to look. Hitler actually wanted war, until he got some inkling of how bad his situation was just before Munich. It was only a (very) active policy on our part that averted it.
I realise this is a bit improbable, and again, I know puplic opinion at the time was strongly against war,
Public opinion was only part of the equation. Chamberlain was for one thing very good at manipulating it; and the euphoric relief after Munich, besides being extensively stage-managed to begin with, faded very rapidly. IIRC, Gallup polls showed the public was much more in favour of making a proper alliance with the Soviets than the government, which would figure.
The appeasement policy was a
policy, based on the belief that German ambitions were if not wholly justified then at least finite, and that by fulfilling them Britain would make Germany part of Europe and thus seal out the Evil Commies. Chamberlain was both a pusher for re-armament and a fairly typical Tory russophobe. Appeasement was not dictated solely by public opinion or military necessity (in fact, Harold Nicholson explicitly said in 1936 "We can beat the Germans with one hand, but that will only help the Evil Commies!")
and armament wise, we couldn't have fought a strong war, but i'm interested in what would happen and had to have happened to bring this about.
In 1936, Germany's army was pathetic. The forces going into the Rhineland were in real terms fairly trivial and had secret orders to run like hell if anyone smelled a Frenchman.
Would we have supported the Republicans in the Spanish civil war?
Almost certainly not, with the same government. The Conservatives could be anti-appeasement (Churchill was tory, after all) but their support for the Franco gang was pretty general (and "non-intervention" was pretty blatantly support for the Nationalists; we even let the Italians get away with torpedoing our ships with a slap on the wrist).
Edit: What would the consequences of Britian losing an early war be? I understand we still had WW1 planes and armament in 1936, would we have lost with these?
In 1936, Germany would have crumpled in a minute. Their army was no more advanced, and piddling by comparison to the French.
Even in 1938, the Germans would go down eventually. The Czech army was, if I'm not wrong, better than the Polish and certainly had better natural defences going for it (Horthy, with Yugoslavia and Romania right there, isn't stupid enough to try anything), and then the Germans stole vast resources from the Czechs, militarily, industrially, and financially.
You've got a smaller, weaker Germany army against the Czechs. If our (lack of) assistance to Poland is anything to go by, they'll still be sqashed before we get our act together, but the Germans will be given a severe bloody nose and barring catastrophe will lose a war of attrition against France and Britain by 1941 at the latest.
That's all keeping the conflict limited, of course. The Italians aren't coming in (except maybe as vultures against Germany in the last minutes), but Poland did a bit of vulturing on the Czechs itself, and the Soviets, as well as being pro-Czech, were very pissed at the Poles. It would require blunders, but a reluctant German-Polish alliance versus CZS and the USSR isn't out of the question.
Edit2: What would be the League of Nations reaction to this? Would Britain be condemned or supported? How would France react?
Our official Rhineland policy was "Bugger.
Prevent the French from doing anything!" We were the brakes on them, not the reverse. They would probably come in on our side after a dither, in the highly unlikely event of unilateral British action.
Britain had pursued a policy of appeasement since about 1870.
Uh, no, we had not. Unless we were appeasing ourselves.