If your dealer is closer than Kwikfit, you could ask Motability that you want to take it to the dealer, due to the dealer being closer.
I imagine the deal Motability have with Kwikfit is cheaper than dealership MOT costs?
Unfotyunately, the car can’t be taken to any MOT station, because Motability won’t have a contract or payment terms set up with them.
I don’t think Motability allow a 3rd service anymore.