Probably a purpose built anti-submarine, convoy escort would be something like the Castle Class. It would look like a destroyer except that it would be slower, carry a different suite of weapons and not be designed for fleet actions.
There is a second alternative, which has already been proposed, which is something along the lines of a D Class Farmile MGB, although bigger (500 tons) and with better sea-keeping.
I wonder though if there is a third alternative. Perhaps at the back of my mind I was thinking of designing something along the lines of a North Sea Oil Rig Supply vessel. Such a ship would have a lot of utility for convoy protection. Such a ship could easily support a destroyer-sized QF gun + some ack-ack and depth charge racks on the stern. They have lots of freeboard forward so good seakeeping. They might even serve as tugs in emergencies.
http://www.pennenergy.com/articles/enlarge_image.cfm?SITEID=os&IMAGE_ID=118286

