WWIII would have to include actors who were willing to expand the theatre to the fringes of Western Europe. That's pretty difficult; it's a lot of terrain, and there's a lot of terrain in-between.
For us to be pulled in "full metal jacket" style, we would probably have to see some sort of Russian non-aggression treaty with China and then Russian/Chinese/Iranian attacks on British bases in Cyprus, including the Troodos communications facility (you take that out and you take out monitoring of all middle-eastern communications by Britain and the US). And that would leave an unholy mess in its wake, considering that Cypriots are largely pro-Russian. But that would be the most likely form of an attack on Britain in the first instance.
What is more likely in Britain in such a scenario is for certain foreign states to agitate a kind of constant low level conflict through proxy agents to disturb British civil society on the ground in their favour.
So you would not be bombed by a nuclear weapon, but you might very well see an uptick in "terrorist" incidents with their funding roots in the Gulf, sudden financial "shocks" caused by other foreign actors playing silly beggars with international finance and sterling trades, the sudden mothballing of works and manufacturers funded by Russian and Chinese finance, street assassinations of certain political individuals, a few contamination scenarios (Litvinenko style), significant cyber attacks that arrest the banking system ... you get the picture.
The other thing that makes us vulnerable is the security of the gas supply. I'm not sure of the current status, but at one point, about ten to fifteen years ago, Russia was supplying the gas for a number of significant locations in Britain. I seem to remember the list included NHS hospitals and, bizarrely enough, York Minster. I hope the situation is different now, as otherwise Russia could just refuse to supply and create chaos. If it does, we've got a significant problem, though the ensuing turbulence in the market would possibly make Scotland very rich.
I do think that there are deep state actors in the US that are sabre-rattling for war against Russia, and it makes me rather nervous because I think there are certain "deep state" figures with a lot of persuasive political power in the US that are completely batshit insane. The US has been a loose cannon for decades in terms of foreign policy, no matter who has been POTUS. Considering that some POTUSes have been distinctly non-interventionist individuals in the first instance (Clinton, Obama, Trump ... yes, Trump), one wonders what the hell is actually going on once these people enter the White House.
Mind you, I'd say the same about the British Foreign Office. It seems to turn Foreign Minsters into absolute loons.