which one of these programs constitute of a military reconnaissance satellite?

None that I'm aware off.

so I assume Britain received its imaging intelligence from the US as part of five eyes. or else I cannot explain how a nuclear armed country has skipped over one of the main prerequisite for missile targeting for 60 years

The UK nuclear arsenal has always been a strategic deterrent. The weapons in the UK arsenal (trident missiles with MIRV warheads) are designed to destroy cities, so unless the Russians have managed to conceal the locations of their major cities, targeting shouldn’t be an issue.

Presumably part of the nuclear doctrine is to take out your enemies nuclear launch sites before they launch

Also, even large cities have places which are better to target

>Presumably part of the nuclear doctrine is to take out your enemies nuclear launch sites before they launch

It is not. The UK, like most nuclear armed states, has a "No first use" doctrine, meaning its nukes exist only to retaliate, to turn cities to ash.

Whoever is nuking you, to the point that you use those retaliatory nukes, might be targeting your weapons, but they are on submarines in friendly waters, so not likely to be destroyed before they can launch.

Your link says:

"The UK’s membership of the European Space Agency (ESA) is not affected by leaving the EU as ESA is not an EU organisation."

I think you meant the EU Space programme, but that does not seem related to military imaging satellites.

Ah, another excellent benefit.