Car dead 2weeks in rejecting advice?

am I within my rights to reject and go elsewhere?

IANAL, but I believe they have the right to try and fix it before you can reject it.

I have given up chasing loan cars a long time ago.  I make other arangements, life is too short, but easy to say in a two car family where we mostly work from home or can use bikes and public transport (by design).

Similiar issue with daughters car, manufacturers recall but no space at dealer to fix it for 3 months and no courtesy car until they assessed it. Spoke to CAB and as its financed she doesnt own the car and its Black Horses problem to sort. one week later it was accepted to dealership and fixed that day. Black Horse were very easy to deal with, far better than dealership.

As if by magic a courtesy car has been found so hopefully things going ok still looking at other cars though

Had similar with a used Auto Cmax (first mistake) a few years ago, it was throwing codes within 2 days of picking it up, internet pointed to a lack of GB oil changes and a likely big bill to fix. The dealers got two bites of the cherry to 'fix' it, first time they claimed it was a driveshaft speed sensor (very obviously just wiped the codes), the car spat it's dummy again within 24hrs, went back again, they then variously claimed it went to ford and/ora gearbox specialist next over the course of about ten days. Who allegedly changed GB oil and 'inspected' it (I was never shown any paperwork or details)... It threw the code again on the drive home when I picked it back up, so I turned around, went back and said I was returning it, followed the next day with an email detailing the history of our dealings and the issues, my expectation of a full refund, for good measure I referenced the SOGA. I was refunded within a day.

My advice, let them have them one go only (don't be a mug like me and let them take multiple stabs at a fixing a lemon) and then be polite but firm, that you're returning the car and expect a refund. Restate it all in an email also, just so it's in some form of writing with a date for later reference...

Remember you're only really dealing with 'flippers' here, however professional the setup seems these are just outfits popping a mark-up on whatever they scored from the car auctions, the last thing they need is to expend lots of time (and cost) failing to fix a car they're only going to have to take back. So they get one chance only, and you want actual details of what is done to it not annecdotes.

Consumer rights act - right to reject in first 30days.

https://www.autotrader.co.uk/content/advice/how-does-the-consumer-rights-act-protect-you-when-you-buy-a-car

Edit- lived experience was threatening to reject a car that was using 1l of oil every 2k miles after they'd twice tried to fix it, ended up a total of £5k warranty work replacing cylinder block pistons etc at a main Volvo dealers.