According to the guidance from Motability, you can either A. Use Kwik Fit at a centre or B. Use Kwik Fit Mobile.
You can use STS Tyre Pros which are owned by Kwik Fit if that’s more convenient.
I would highly doubt that they would allow you to use ATS because Motability wouldn’t have a trade account with them and therefore payment would be difficult and it would be outside of their recommendations. It’s worth a call though.