Faulty car bought from garage but I have spent money on it...

sweetsand

You bought the car a few days ago then had it serviced?
Did the garge not give a minimum period of mot & service?
If not, then as far as garages go they are making you  good offer.
Main dealers are very expensive but we will only buy from a main dealer as they
normally seel good cars and will fix if any problems.

macman

You bought an old, high-mileage car from a garage without any documented service history. Would it not have been advisable to ask when it was last serviced, and then ask for a service to be done before delivery, if it was due? 
You have another 21 days to reject it outright under CRA 2015. If they've offered you a full refund already, I'd tear their hand off, and consider the £380 lost as a relatively cheap lesson in how not to buy a used car. 
It's your job to do due diligence, not theirs.
PS: the non-appearing 6m insurance based warranties are next to useless, as almost any component likely to fail will be excluded. But, again, why did you pay for the vehicle without receipt of the warranty?