A few thoughts:
* First of all, it's highly implausible that the USSR would allow Britain (and presumably France) to keep their nuclear deterrent intact. If the Soviets are going all out, all the nuclear powers get targeted. There's nothing to gain from allowing anyone to hold significant nukes, particularly countries that have been on the opposite side of the Cold War of them since Jump Street. They'd be more likely to attempt to go after Europe in a nuclear/conventional war in an attempt to turn the whole continent red (proverbially or literally), making the offer to the U.S. to stay out of it in exchange for no exchange. But Reagan would tell whoever it was making the offer to cram it with 10MT walnuts and we'd have our global thermonuclear war anyway.
* But taking what's been proposed at face value: Cynical as it may sound, Britain is of more use to the U.S. by playing neutral right now than it would be if she launched her missiles. News of Britain's "neutrality" won't get to the U.S. for some time because the Emergency Action Notification will lock down the media and be broadcasting news and instruction on the impending holocaust. An intact Britain (and France) can help the U.S. recover, and the USSR will likely be done as a nation. Of course, there's nothing keeping the Soviets from breaking their word and launching at Europe anyway. After the fact, Britain will still have their deterrent on hair-trigger alert because nobody will know how many nukes the now-former Soviets have, or who's controlling them, or what they might do with them. Still, the only way Britain can help the U.S. is after the exchange -- even if they launched the moment Thatcher had Popov escorted off the grounds, they won't be saving any lives at that point. It'll look callous to the point of traitorous, but in the final equation, it's the, ahem, best-case scenario for the Allies.
* If Popov is any relation to the makers of the most reprehensible vodka ever created, he should be shot on sight for war crimes against the world's livers and taste buds. There's a reason you can get that shit for 8 bucks a half-gallon.