The Peregrine developed 0.68hp/cuin. Projecting development to the best performing late war engines (.9hp/cuin) the Peregrine only develops 1100hp - 1200hp. Thats still fairly low for a mid war high performing fighter. In addition, you have increased fuel consumption without addressing the limited fuel capacity/short range.I like this, and if we can keep the Peregrine's dimensions and weight down, we might have an engine for a lightweight, smaller single-engined fighter. I'd want to offshore the engine production away from RR though (and likely the aircraft as well), as they clearly don't have the capacity to produce more than one engine type at a time. The Griffon came on board after years of expansion.
Going completely off timeline, I could imagine an argument where a turboprop replacement for the Peregrine would be a promising avenue.