Read the scenario again, it's completely up to the scenario designer to dictate the rules because it clearly has nothing, or very little, to do with historical events (as they happened). So 1200 262s is also, a irrelevant number.
Fact remains that the germans pushed jet a/c into service earlier than the allies, while the allies relied more on proven technology used in numbers. Had the situation been as in this scenario, jet a/c would no doubt have taken priority in development on the allied side as well. However, the German Me262 was a superior design at the time. With its swept wing it was more aerodynamically advanced than the US P80 and the British Meteor. Had the Germans laid their priorities right, they could have fielded the 262 in 1943, while the allies may have been able to match that service date (roughly, I don't know enough of their development to tell but let's assume they could have) with their own jet fighters, the 262 was at the time the most advanced design.
Given the conditions of this scenario, it seems the U-boot war in the atlantic is playing out in favor of the germans. So it wouldn't be odd if supplies were scarce on the British isles.
It is a kind of a "nightmare" scenario for the allies. So what, do people have a problem with that?