Any way you shake it an arms race had developed between Germany and GB/France by 1938. The Germans had gotten the jump on it without doubt but orders placed alone clearly shows both French and British seriousness. TBH I'm of the opinion that the Germans struck at the absolute hot minute in 1940. By 1944 the western allies would have been bristling with arms and logistics. The notion of a daydreaming and peaceful Britain ignores the orders placed, the factories being laid down, the radar antennas. You don't build that revolutionary of a system without a very real doubt to drive it.
Fundamentally the voter base in France and GB didn't want war with the Germans again. But they also were not going to dismiss the German threat easily with so many of their brothers and fathers in the ground from the Great War. Politics would spur the arms race on through 1944 handily. Chamberlain was a politician, not an idealist, if the base wanted arms and peace, arms they would have and peace they would be promised.
All the while I believe the Americans would happily play the grocer to the French and Commonwealth arms build up. Either with arms directly or raw materials on credit.