WRT the Soviet invasion and the sea-faring stuff, it boils down to who has what still intact at the time the invasion is staged. Even if the RN, for example, had little to do WRT to mobilising for the war effort (aside from it's submarines), it's likely that they would've been subject to nuclear attack whilst in port or at sea by various conventional elements of the VVS. I also wonder why this same thing hasn't happened to the Soviet navy. Even if various navies had survived as elements between Scandinavia and the UK, the Soviet ships would - as has been pointed out - have to run the gauntlet. Not only that, but they'd have a pretty difficult time not being blown up by various mines.
WRT an amphibious capability, IIRC the Soviets did have that in various forms so it could be part of any flotilla. At a stretch I guess VDV aircraft might possibly get from Murmansk to perhaps Scotland if they were careful and had enough support. But I don't see what they'd be attacking or hoping to achieve. I don't know why they would be in what used to London, fighting a 'home guard'.
As I've said before, previous treatments in T2K WRT the UK are, I'm guessing, written from an American perspective and so in that sense the UK is seen as a relatively small place. However, even if you managed to somehow get a whole VDV division into the UK, it would be swallowed up fairly quickly just by the general post-war terrain and other factors. And sooner or later they'd simply run out of supplies.