Unless the UK wants to build an all-new platform, Japan-style, there isn't going to be an all-UK MPA. Even the brain of the MRA4 was from Seattle.
On the other hand, there's a lot of scope for UK content in the acoustics and radar systems, and with its experience in ASW/MPA, the UK could lead a program that might (if done properly) fill a few national needs, doing a large percentage of the P-8A mission for a small percentage of the cost.
Displays, computing, lighter and better radars and other technologies (like electric torpedoes that don't have to be carried in a bay) can give you a bit more effectiveness in a small package. And props are more efficient than fans in this regime. Also, before anyone falls over laughing at the Q400 idea, the Q400 has >80 per cent of the payload-range of the Lockheed L-188, which IIRC turned out OK as the basis for an MPA.
Difficulty: ASW. Both MRA4 and P-8A were big and expensive, in large measure, because they are designed to carry a metric
ton of sonobuoys to do multistatic active coherent (MAC) acoustics, which may be necessary to hunt AIP boats and modern nukes. How does a smaller aircraft handle that?