Buttler BSP Vol. 3 Fighters & Bombers 1935 - 1950, states explicitly
that the Kestrel K.26 (Peregrine) was picked at the beginning.
The Putnam Westland Aircraft since 1915, and Goulding's Interceptor,
state the same.
The Kestrel XVI would most likely be the best match fotr your idea:
670 hp at 2,225 rpm for takeoff
690 hp at 2,600 rpm at 11,000 ft (continuous power, medium supercharged))
745 hp at 3,000 rpm at 14,500 ft (Max emergency power, fully supercharged))