Some of these are going to have to become unitary authorities - places like Rutland, Westmoreland and Huntingdonshire; many of the less populous and geographically small Scottish counties; Anglesey, Meirionnydd, Montgomery, Radnor and Brecon in Wales.
Yorkshire might end up with some kind of mezzanine system, with the three ridings acting as sub-counties. Lancashire might need something like that itself.
As for the larger cities, there might be separate Metro Boards, which act to coordinate services across county lines.