As others have said, KwickFit is the preferred tyre service for Motability, but they will allow dealers to do it if they are there or thereabouts to KwickFit’s price. I hate KwickFit. They are lazy in how they do things, such as levering off wheel badge centres, rather than pushing them off from behind as they should. Well over 2 years into our lease and I don’t have so much as a minor scratch on any of the four alloys, yet I know they would manage to scratch at least one. It always annoys me how they get the wheels so filthy as well and never wipe them off. Your tyre is down to the tread wear indicator though, so needs doing urgently.
As for mileages from tyres, how long is a piece of string? It varies enormously by tyre type, car and driving style. In my younger days, with a heavier right foot, I rarely got more than 10,000 mikes from tyres. Now I can often manage 30,000 miles ?