Alsch91 is right. UK only needs to build infantry in London if Germany puts up a credible sea lion threat. Once the threat is over they can build elsewhere and just let the London IC sit damaged.
Many turns later, those UK infantry that were built on round 1 may reinforce an American landing in Normandy/Holland. They can be picked up by transports that were built in Canada, perhaps with some Canadian built artillery units already on board, and dropped wherever the Americans just landed. There is little need to build much in UK if Germany wants to keep strategic bombing