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There was supposedly a very real suspicion amongst the security services that Harald Wilson was working for the Soviets. Personally I think it's very unlikely, though some of his cabinet I'm less sure about.

Let's for the moment imagine it was true.

It's Easter 1965 and following the arrest of a British agent of the KGB, in the hope of getting a lighter sentance the agent names those who he had at one time recruited. One of those names is Harald Wilson. Now obviously the police (and others who don't officially exist) would be sceptical but the would have to (carefully) investigate the allegations. The investigators over the next few weeks turn up more and more evidence until in late August they have enough that had it been anyone else they would have been arrested. Due to it being the P.M. the option of contacting the Home Secretary is not feasible. The whole cabinet is potentially compromised. With no other option the Queen has to be informed.

She with such advice as is available then calls Wilson to the palace and as is at least in theory her right dismisses him, following which he is arrested. Now I know that in all likely hood it is much more likely he would be told she accepts the resignation he hasn't given yet and he would then spend the next few years being debriefed, and the public would never know but if he had been arrested and charged what would happen after the news broke?
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