As far as I'm aware they don't seem to have been preserved unless they were kept by individual officers, in which case the odd one may be still in the hands of family members somewhere, or donated to some local museum. In the case of MGB 658 for instance, Len Reynolds
, who was the last officer of the boat, first published Gunboat 658 way back in 1955, but I don't recall any mention of his having the ship's log, and I don't believe it forms part of the archive of research for his three volumes on Coastal Forces history, which he deposited with the Imperial War Museum. I saw the ones for MTB 85 there once, which do form part of his papers, and which were passed to him by its Commander, H F Cooper, with whom he co-wrote one of the books. There are two of them, which are large A3 type sized books, but they mainly cover the day to day movements of the boat and its location. The action reports for a boat are a separate thing.
Anything still in existence is with the National Archive
in the main, which does have logs for some of the later boats retained after the war, up until the official disbandment of Coastal Forces in 1957. Peter's log, which he posted, is a diary he kept himself I understand.
There's also the Naval Historical Branch
, but I'm not all together sure what they hold, and what they may have already passed on to the National Archive.