Mark I boats had the same leaky issues at the port locker and lazarette. The main website had an FAQ on this hundreds of years ago: use weatherstripping. You could use 3/8 inch foam from a hardware store, or go to an automotive store and get really good rubber stripping.
It's worked for us and may work for you, but I am not that familiar with the details of the rims of the lockers on your Mark II.
It's worked for us and may work for you, but I am not that familiar with the details of the rims of the lockers on your Mark II.