As UK you're not forced to accept anyone in the Allies, since you're faction leader.
Just ignore the repeated 'could we get in message', and you're just fine.
However, beating the axis with 300k men is only possible with >70% Armored/Mechanized or heavy 100+ wings air cover (if USSR spanked Germany already very hard you might be able with 300k infantry)
My BEF is 70% Infantry+ART or AT divisions, but i plan to build a second BEF, so no worries.
My question is: will Japan declare war on me, even if the US are not in the allies?