It's a popular counter factual: The Eagle has Landed is set a little later in the war, but there are other books and films in which steely-eyed bands of elite German troops engage in derring-do in the English greensward.

There's three questions here, one of which I will leave to others: what, if any, plans did the Germans actually construct? To me, the two more pertinent questions are (a) would the Germans have had the practical capability to launch such a mission at any point in the war and (b) had it succeeded, what would the practical effect have been?

German espionage in Britain was a disaster. It was incompetent, insecure and ineffective. Post-war records show that there were no successful landings in England by Abwehr agents (the book you want on this is Macintyre's "Double Cross"). Breaking Enigma helped, but agents weren't carrying large cipher systems with them: all the hand ciphers had been broken as well. The agents were low-quality, badly equipped and trained, and immediately detected and, when not quietly executed, turned. The chances of the Abwehr being able to build the infrastructure to land and operate an effective unit to carry out an assassination of kidnapping were approximately zero and yet further declining with every captured agent.

When Heydrich was assassinated, Czech troops from the army in exile were able to move amongst Czech civilians like Mao's fish in the sea; Abwehr agents were more like whales in Trafalgar Square. The Abwehr did not have convincing English speakers, there was (for practical purposes) to German-sympathising Fifth Column in England...it's a hugely different task for an army in exile to operate in its native, occupied country as compared to foreign agents operating in a foreign country where it enjoys no popular support.

But assume, arguendo, that Germany could have inserted a serious assassination team into England and kill Churchill (at the time one of the most heavily protected targets in the country). What would have been the political effect? By the time Churchill becomes Prime Minister in May 1940, in the aftermath of the Norway Debate the (for want of a better phrase) "peace faction" was pretty much discredited. Chamberlain had fallen not because he wanted to surrender, but because he was perceived as not pursuing the war adequately.

So who would have actively sued for peace had they been in power? There were traitors like Mosley, who was interned within two weeks of Churchill coming to power, but they had no public, political or parliamentary power. So the obvious answer is Halifax, who actually did propose negotiating with Hitler via Mussolini during May 1940 and had been a serious contender to replace Chamberlain until Churchill prevailed. But Halifax had little support in either the war cabinet or the wider main cabinet in his desire for peace, and although constitutionally there is no bar on a Prime Minister not being an MP (cf. Lord Salisbury, who was Prime Minister into the 20th century) it was a major reason why Halifax declined.

So the hypothesis would be that in the aftermath of Churchill being violently killed, the British population, parliament and the cabinet would have agreed not only to a Prime Minister who was not an MP, but also was not the leader of any party, and would then agree to his pursing a policy direction which had been university rejected in cabinet, implicitly rejected in Parliament ("I speak for the fighting Navy...You have sat too long here for any good you have been doing...etc") and would have had very little support in the country. ANd if not Halifax, then perhaps a revival of Chamberlain, who had recently resigned and would die within six months anyway (he resigned in September, with colon cancer). It doesn't seem terribly likely.

Who would have replaced Churchill had he, say, had one stiff martini too many and stepped under a bus? That's a topic for speculation. Eden? Attlee? It's another discussion. But it wouldn't be Halifax (already rejected, not an MP) and it wouldn't be Chamberlain (sick or dead), so that's the peace faction gone.

So there's the summary, I think. The Germans couldn't have mounted such an operation, but if they had, they'd have ended up with a "war" British PM, not an appeaser.