Its a used car and the issue has been identified as an O2 sensor which can fail without warning i.e. you cant really check them for wear and tear like brake pads.
In what way is the dealer dragging their heels? You stated they are willing to fix the problem and supply a courtesy car while they do this.
I am going to be blunt - you won't get a refund based on the owner history and trying to get a refund for something like the fault above won't happen until the dealer is given a chance to fix an UNFORESEEABLE FAULT with a USED CAR.
Even brand new cars can have faults.
I advise taking a step back from the situation, take a deep breath and come at it with the blinkers off.
Under SOGA I could have rejected the car for a full refund due to the fault occurring so soon after purchase.
The dealer does not need to be given an opportunity to fix the car if the vehicle suffers a serious fault or issue within a 'reasonable' timescale.
I only know that it is an O2 sensor because a friend has an OBDII connector and checked the fault code for me. Coupled with the the Engine Management Light is the intermittent and difficulty starting the vehicle. This often means it takes me around five to ten minutes to start the car, this to me, is not a minor fault.
Anyway, I chose not to reject the car under SOGA and allow the dealer the opportunity to fix the car as they made all the right noises.
Fast forward three weeks and my car still hasn't been looked at by the dealer. So that is what I mean by dragging their heels..... I think they are hoping I just go away.
The V5C was the final straw and again under the Misrepresentation Act 1967 I probably could pursue for a refund, but it would likely go to Court and who knows what the outcome would be, though my legal advice seem to suggest I have a good chance.
However, I am not prepared to go down that route because of the hassle involved. I don't need to take a step back, I'm not angry, merely frustrated and aware of my consumer rights.
Totally appreciate cars develop faults, not a fool, but three weeks later, no fix, no repair, I think I am pretty well within my rights to be frustrated and looking at options.