Does the dealer advertised a '1001 point health check' as part of the prep of their vehicles? If so time to get back in touch and tell them it shoukd be 1005 as they appear to have missed the brakes on your car,

I would also avoid Kwikfit, especially on a car you ahve just purcahsed. Far better to go to the Mini dealership.

Grinding suggests pad material gone and metal to metal, so yes it probably does need new discs.

Not sure i'd be using the workshop mentioned, as alluded to above it probably needs a jolly good full brake service, which in my humble means DIY (best of all) or using a good competent indy who knows how to, and is interested enough in quality work, to do this most important job properly..

Get the fronts looked at too.

The dealer should do the job for you if they have some honour, you'll know minutes after contacting them if they have any.

Had you taken it back to the selling dealer I’d say yes, it’s very likely they’d replace the discs if and I repeat if they actually needed changing. You didn’t however give them a chance to check it. This fast fit chain like many others are notorious for up selling, telling you that something needs replacing when it has plenty of life left in it. Their staff are on commission which to me should be illegal in the motor trade. I’ve had a few customers return to me with cars they’ve been told by this chain while they were in for a puncture that they needed new shocks or brakes only for me to send it to the workshop I used and no fault to be found. I wouldn’t use them if they were the last garage on the planet.

Agree with everything SLO said above. You needed to give the selling dealer the chance to fix it before involving another garage. This is the problem when buying from dealers that aren't local.

Did it come with a fresh MOT when it was bought? Was there any advisories for the brakes? Did the work really need done?

As others have said, KF might not be the best bet for the work. However I assume you’ll have paid upwards of £11k for the car, for all the angst pursuing the dealer is likely to cause I’d just suck up the £240.