You really should try to hold London if at all possible and only use the knock out of the German navy as a fall back.
Bring the med fleet including the transport carrying 2 inf or at least 1 inf 1 aa gun to gibraltar with the intent of landing troops back in the UK and stationing the consolidated fleet in 110. If the Canadian navy survives, that’s two more troops that can reinforce.
The Germans will need to hit your fleet on the same turn that they invade or else they will lose their navy the next round when you counter attack it. If nothing else, the threat of the scramble defense will force the germans to assign some luftwaffe units to the sea rather than the land, and this boosts your defensive odds. You also cancel the bombardment shots.
Activate Ireland with your mech inf round 1 to create another landing spot for US bombers.
Obviously max infantry builds with UK for R1 and R2.
Get 1 or 2 american carriers stationed in SZ 102 on R2 so that you can hit the German fleet with bombers and ftrs/tacs after the invasion.
Yes, the best way to liberate the UK is to take care of that massive german transport fleet first. If you don’t take care of it, Germany might get to take UK twice, which is a disaster.