Have you not tryed speaking to Motability about not having any confidence in the car in adverse weather conditions due to the tyres. If the car got you home it should get you to kwik fit the main issue would be if you doing high speed driving. But rac will sort it now you contacted them..
A tip if you ever get a blowout at higher speeds do not brake or turn the steering wheel keep it going in the direction you going and come to coasting stop if safe or if on motorway move over once you slowed enough.