Pete - these are no longer the days when we have the largest navy in the world, a strong air force and a large army with a larger pool of reservists. We have, at least publicly, no long range air defences apart from the RAF (no significant SAM net). We no longer have much defence production, nor do we have much of an industrial base that could be turned into defence production. Our political leadership has the unfortunate habit of being both belligerent and clueless, and even worse they are actively rigging the system so that it would be very difficult to remove them in an emergency (unless there was action by the military or security services). Our populace is both unarmed and untrained in arms for the most part, with a low level of general fitness and whilst there is a lot of social cohesion still, a lot of the effort of the current rulers is aimed directly at undermining that. The country is in a large amount of debt, much of it to the people who have caused the debt and who now profit by it.
If NATO were to collapse and the EU encouraged to stay out of it, we'd be left utterly exposed - far more so than in June 1940.
If that fact didn't itself cause a government to collapse in the face of Russian aggression, I would imagine any invasion would start with some shocking act that we couldn't respond to - a tactical nuke or maybe just a massive conventional missile attack on RAF bases away from cities, something below the line of the "deterrent" being used (which would of course mean the deaths of nearly everyone on these islands) but enough to make it obvious what further resistance would involve.
Then they'd probably be happy with some compliant regime doing their bidding - perhaps with "advisors" who would fly in and have a very comfortable time at our expense whilst protecting them from the resistance-Nazis who would spring up. I would imagine you would recognise many of the people making up that regime.