i want to say river class frigate, but that's probably not correct.
Yep, River class frigate is not correct...
Flower-class corvette?
my hunch is a coast guard cutter, 1950s or 60s.
Rebuilt/modified Loch/Bay class frigate?
Guns and bridge seems to be brittish, but I cant come up with any similar size desing with flush deck like in US DDEs. So my suggestion is US DDE type in RN (or colonial) service modified to minesweeping?