Black Swan sloops became prolific submarine hunters

Did the Royal Navy have an equivalent to USS England's record of sinking multiple submarines?

Yes: several Black Swan-class sloops and hunter-killer groups achieved repeated submarine kills, with some Flower-class corvettes also recording high totals.

Britain had several escorts and groups comparable in effect to USS England. Black Swan-class sloops accumulated repeated submarine kills while serving in hunter-killer formations. Some Flower-class corvettes also achieved unusually high totals. A joking suggestion that these groups seemed to have a direct line to Bletchley Park points to the value of intelligence in knowing where to search. Their records connect the interwar sloop design lineage to mature wartime ASW operations.