I concur with Jheiminga, in that available or proposed engines would be called up in a new design and the airframe is built around it and the other key requirements of the contract. Significant modifications could then be assessed for a different engine type but would ultimately proven by flight test.
As stated above, some engine/airframe combinations were much more successful: the Hercules powered Halifax and Beaufighter than the Merlin-powered versions, for instance. The Hawker Tempest flew with both the Napier Sabre (Mk.V) and Bristol Centaurus(II) and both were extremely capable.