Lord Halifax would be the major one.

He was in line to become Prime Minister after Chamberlain resigned but declined, partly because he felt Churchill would be a better wartime leader, but more particularly because he thought with Churchill in charge of defence he'd become a figurehead or be ousted (a la Asquith and Lloyd George in WWI).

He advocated peace talks in 1940 but lost out in the cabinet debates to Churchill. Halifax wanted to give up more or less anything to preserve British independence and they were feeling out the italians as mediators.

Churchill convinced the cabinet and the rest is as they say, history.

King Edward VIII, not a "politician" but as head of state, had Nazi/Fascist sympathies. He was certainly limited in how much sway he had over the government of the country (if any at all), but there certainly would have been a concern of him leaking state and possible military secrets to Germany, even if unintentionally.

Fortunately, Edward VIII abdicated before war was declared. In reality even had he not abdicated, there would have been substantial pressure for him to do so. And he would have been kept even more in the dark than monarchs usually were, but the morale damage would be enough. It is suspected in his post-abdication role as the Duke of Windsor he informed some Nazi agents, but I don't believe that has ever been proven.

This question interests me greatly. As a follow up, do we have any indication how a peace negotiation at this point would have been received in Germany? Were there any in Germany who expected such to happen?