You still have not demonstrated Britain would have gave up. The fact they supported sending men to Finland shows that the Anglo-French alliance were consigned to fighting both the Germans and the Russians.
Your presumption is that once France falls, Britain's internal calculus changes. However, you arbitrarily decide Britain merely makes piece with their enemy to pile on Germany (which is your dream scenario in every thread.) Of course, this makes no sense being that Britain was just bombing Russia. To suddenly stop and make overtures for an alliance as soon as France falls connotes major weakness, not that of a multi-continental Empire which just a few weeks before it can contain both Germany and Russia, no problem.
If Britain is that weak where they must suddenly disengage, then why even continue fighting at all? Why not make peace with both the Germans and the Russians? And, are the Russians going to stop for absolutely no concessions? IOTL, they had eyes on British territories in the middle east and central asia. Britain engaging Russia in a warm war provides the cassus belli for Stalin to achieve his territorial designs which he attempted to achieve IOTL in the Axis pact negotiations.
The more likely scenario is if France falls, the war looks incredibly hopeless and Britain will simply make peace with both Germany and Russia. IOTL, Italy thought Britain would simply quit after the France debacle. Mussolini was not a maniac, though he judged wrong. Add the fact that Russia is at war with both Germany and Russia, it is almost assured Britain makes peace.
___
Ironically, in the events above, the likely result is that the Germans go full retard and invade Russia. And, as soon as that happens, it is possible the Britain rejoins the war to help Russia. However, I do not even think this is very likely as IOTL the Brits and Americans expected Russia to lose. This means that Britain only re-starts the war if they think the US is going to be involved, which might not happen because Britain is out and with peace between 40-41, the Dutch will be selling oil to the Japanese precluding the need to invade them thus butterflying away Pearl Harbor.
So, Britain likely sits out even as Russia probably avoids defeat at the gates of Moscow (though IOTL British lend lease might have been the grain of rice that tipped the scales in Russia's favor in repulsing AGC.) This means Russia cannot successfully decimate AGC and the result is without enough promise to win the war they only get minimal assistance from Britain and America. By 1943, Russia simply runs out of men and food to keep fighting.
___
In short, French in Finland and British bombers over Baku loses the war for Britain and likely ends up in the Soviets being beaten by the Germans in continental Europe.