I used to live and work in Hull for many years, can highly recomend Richard at Savoy Tyres just off the old Hedon on there advert i think it's called the city centre branch. If you do meet Richard tell him Shadrack says hello.
No re3commendation implied but you might try asking Traveller Timbers at Little Weighton - who seem to cover MOT repairs to Minors - who they use if they need an MOT. Here's the link to their website:
Yes - North Moor Garage in Cottingham. Took my Allegro there for a suspension pump-up, it's a proper old-school garage in a big old shed type building. The guy used to work on all the old cars (he looked to be in his 60s) so he knows all about them.
They were very helpful and very reasonably priced.