NATO has collapsed. The Russian army is marching through Europe unopposed. The French nukes being under EU control is just your EU hate coming through - I mean seriously the French would just tell the EU to fuck off - but okay I'll give you that one. Now so far so good but here is the kicker. Under your scenario Russia is taking Western Europe with token resistance so why the hell would they bother launching a nuclear strike on the UK? Makes zero sense. So far the Americans are staying well out of it so why ratchet up the ante from conventional to nuclear? Furthermore you say French nukes are off the table. Well nuking the UK puts them right back on the table given France is only 22 miles away. The EU maybe slow to decide but mushroom clouds on the horizon and fallout over Western Europe would probably bring a quick consensus.
I get you have gone for a doomsday scenario; NATO collapsing, EU all but gone, Americans out for some unspecified reason but it's still makes no sense to nuke the one country that could retaliate. It also doesn't say much for 'Trident the deterrent' argument. All it seems to have done is put a big bullseye over the UK.