Court of arbitration

So let me try and explain this as best I can.

So I bought a 5 year old car from a dealer end of Oct 2019, one owner and full service history.

There was a tyre pressure sensor light on the dash when I test drove, salesman said that would be cleared it just needed to be re trained, also noticed it was down on power a lot and I put it down to the new car being a 1.7 estate as opposed to the 1.9 octavia I was trading in.

Few days driving and I knew there was something wrong, so I e mailed the garage, they had the car back a few times but couldn't find anything wrong.

Jump to December and the car over heated on the way home from work. Garage took car to main dealers to investigate, and they rang me to say that the head gasket was gone. They agreed to replace the engine with a second hand one, which they did. I asked for the reg of the car engine came out of for verification of mileage, bilut they said they couldn't because of GDPR.

So the engine change took 6 weeks, and that was only because I was chasing down the garage that were doing the engine change, dealer didn't have there own mechanic.

Went to collect the car and the back bumper was driven in, looks like it had been reversed into a wall, so the dealer agreed that they would fix that.

I had to make 3-4 more visits to the mechanic as coolant level kept dropping, but he eventually found a loose pipe clip and that seemed to solve it.

Cue 4 weeks later, and I'm driving home and the car goes into limp mode and engine management light is flashing off the dash. (I took video of dash) so dealer has car towed and they ring me a few days later to say the car is driving fine and there's no fault stored on the memory. There denying breakdown ever happened.

So myself and my wife discuss it and decide the car is not reliable, and too dangerous to keep. I tell dealer I'd like to return it under warranty, and they refuse. So I contact solicitor.

So now to the nub of the problem, the other side are using "without prejudice save as to costs" letters in all there correspondence with me.

They have accused me of causing 3500 worth of damage that was either on the car when boughtor simply didn't exist, ie small scratches, roof rails pulled up, accused me of having roof racks and ladders on roof, damage underneath car, all of which meant I had to get an engineer to check the car. And lots of letters back and forth between solicitors, and all the while racking up my costs.

I later also confirmed from the lease company that owned the car prior to the dealership buying it through auction, that the engine and radiator were melted and were beyond economical repair. And that the garage that ran the diagnostics test on the car after it went into limp mode, also did the pre sale service of it.

Now forward on to the eve of paying for the arbitrator, and there offering the full amount paid for the car back, but not my costs which are currently about 3000. This seems to me to be an arse covering move on there behalf.

Now could this be considered an abuse of the "save as to costs" tool, which is meant for genuine negotiations between parties?

How can they argue for 12 months, and then not agree to cover costs aswell?

Has there ever been a case where the without prejudice letters can be introduced during the case?