Looking at the photos, I think there are three possibilities
1) BYMS (British Yard Mine Sweeper) Class minesweepers. These were built in large numbers in the USA for both the US and UK Navies. The Royal Navy had 150 supplied under Lend-Lease. They weren't given names, the most famous of these, J-826 became (eventually) Jacques Couseau's ship 'Calypso'. Being supplied under Lend-Lease, all the ships would have been returned to the USA after the war ended. These were 136 feet long and displaced 270 tons.
2) MMS Type (Motor Mine Sweeper). 400-odd of these were built for the RN during the war. They were not powerful enough to tow standard minesweeping gear, so were used specifically to hunt and destroy magnetic and accoustic mines. Thes were slightly smaller than the BYMS type, but I always thought that they were 'sharp' at both ends. Their usefulness was very limited and they had all been disposed of by 1947.
3) Discounting the WWII theory, they could be 'Ton' class. 119 of these were built for the RN during the 1950s and several of them were disposed of in the Swale. They looked similar to the later batch of BYMS ships, but were bigger, being 152 feet long and displacing 440 tons.
There are other possibilities, Bangor or Algerine classes spring to mind, but they were a lot bigger, being over 1000 tons displacement and over 200 feet long for the Algerine Class, and 600-odd tons and 171 feet for the Bangors.
Without seeing the wrecks for myself, it's difficult to say what they actually are, what I've given here is intended as a guide to what they could be.
Are we sure they're Minesweepers?