I've read that MOTs on commercial vehicles have been relaxed/suspended for now, and that a statement will be made on non-commercial vehicles soon (or words to that effect)
From BBC Website:-
Garages are allowed to remain open under the new restrictions. MOTs have been suspended for lorries, buses and trailers for up to three months, and MOT testing for cars, motorcycles and light vans is under review.
The Driver and Vehicle Standards Agency (DVSA) has also
suspended driving and motorcycle tests in England, Scotland and Wales for up to three months from 21 March 2020, except for critical workers.
All practical driving tests are also currently
suspended in Northern Ireland until 22 June 2020.