You need insurance and then you have to pre book the MOT. You can then drive to / from the place of MOT but you might not be able to drive back if it fails with a dangerous problem.

Also it will need to be insured in its own right. You can’t drive it under the driving other cars provision if you (or a friend) have insurance for another vehicle. You would have to add it temporarily to the other car’s policy or buy short term insurance. It’s not stated if the MoT has expired but you would have to ensure the cover allows for this. It must be a common occurrence so it’s probably not an issue but just bumps up the premium.

Another option might be for the garage to collect under their insurance if they have the right cover?