Harrier III? F-35B alternative fantasy

Carrying on from certain other threads here, I would like to invite comments & suggestions on the feasibility (technical, not political – I realise that’s approximately zero) of a British-led STOVL alternative to the F-35B. It need not have anything in common with the Harrier, except for STOVL capability.

Gentlemen, here is your remit:

BAe have been contracted to produce a feasibility study of such a plane. In order to minimize time & cost of development, they are required to use hardware which already exists or is under development for other aircraft wherever possible, so no development of new radar, engines, etc. It should be, as far as possible, immune to US technology transfer restrictions, so US components should only be incorporated where it is believed there will be no issues with support, upgrading or integration. Consideration should be given to export potential, so suitability for existing & potential operators of ships capable of carrying STOVL aircraft should be taken into account (e.g. it should fit Cavour). Risk-taking partners are welcome, as long as they don’t compromise the basic brief, to produce a plane for the RN & RAF, & design leadership remains with BAe.

Back of fag packet cost & timescale estimates, please, with proposed weights, performance, main systems (radar, other sensors, weapons, engine(s), etc), suppliers, potential development partners & customers. And proposed names. We never did put a Kestrel into service, did we?