Issue with car within week of purchase - England

I purchased a used car (40,000 miles, if that’s relevant!) last week and collected the car on Saturday, it came from a national dealership. Today (Friday) whilst driving an engine warning light has come on and I have read the code to be a turbo issue. I immediately contacted the seller and reported the issue, asking them to look into the fault.

(I had also purchased additional warranty coverage for the vehicle)

They have responded and said the soonest they can have it in to be looked at is the 15th February. This feels like an exceptionally long period of time. Where do I stand in regards to my rights? Is there a time limit on which they should attempt the repair?