Churchill had arranged operation Fish, having all the wealth of the UK (gold, securities) moved to Canada. The gold was to be kept in Ottawa and the securities under the Sun life building in Montréal. The British thought that Canada was a safest place for their gold. One might speculate that in case of imminent invasion, the Royal family and the government would have followed the gold.
Reading Paul Reid's & William Manchester's The Last Lion: Defender of the Realm, 1940-1965, Churchill was supremely confident the Germans unambiguously lacked the capability of mounting a successful invasion of Great Britain. I think the most telling example of this belief was the decision to send men and matériel from the island to support the war efforts in North Africa, even while the Battle of Britain was on everyone's mind. The fiery rhetoric about bonking the heads of Germans on the British beaches was more a matter of reinforcing British resolve and morale.
In short, it's difficult to answer what Churchill would do if Great Britian were successfully invaded because he was so confident the Germans lacked the capacity to do so. For what it's worth, a last stand implies the imminently conquered opponent has nowhere to go/nothing to hope for. Even if the islands fell, Churchill could have counted on the remnants of the British Empire, the USSR, and the US to continue the war.
A side note - there is a series of programs that tells the story of Churchill's bodyguard, Walter Thompson. The two men spent much time together and Thompson saved Churchill from harm on several occasions.
I forget the exact words, but in one episode Churchill intimated that should the Germans "come for him", he wouldn't be taken alive. He carried a colt revolver and according to Thompson was a pretty good shot. Of course its pretty unlikely that he'd ever be left in such a situation but Churchill did have a tendency to get into potentially dangerous situations.