As for UK, i wouldn’t give GErmany any gifts…
Losing London is not good, and remember, even when USA liberates it later, it takes 1 more turn before UK can buy anything + american fighters can’t land for defence. And Germany most probably still has its transports left, so they can just take it back again and loot the UK one more time, gaining more IPC’s than if it would not have been liberated.
Also the Allies lose alot of time with this (not only Axis) and while London is down, there aren’t any reinforcements in South Africa. Good for Italy!
So basically, for the UK: buy defence first and when it is safe you can start building fleet and air force (and tend to South Africa). All those defending infantry will come in handy later.