Dealer unable to resolve leak after 3 attempts - despite insisting on repairing it themselves

I bought a car a few months ago and noticed within 30 days that it was juddering when turning upon start up and when braking.

Told the dealer about it and they insisted they would not pay for a repair at a local garage but would instead pick the car up and repair it at their garage. I agreed as they didn't give me a choice and they picked the car up and drove 250 miles to their garage and replaced the power steering pump before driving 250miles back.

A few days later, the problem re-emerges so I checked the power steering reservoir and it was near empty. Told the dealer and they once again refused to pay for a repair at a specialist locally picked it up to repair again.

This happened one extra time after at which point I was completely fed up and felt really mugged off. I then decided to cough up and get the problem fixed at a local specialist which cost me £250. The dealer I bought the car from is now ignoring me when I asked them to reimburse me for the repair so I'd like to know what options I have.

I'm not looking to get compensated for the 1500+ miles they've added to my car but I would like them to cover the cost of the fluid repair as their garage clearly couldn't diagnose the problem like my local specialist could.

The dealership is an independent second hand car dealer and not on any of the motor ombudsman lists so is my only option to bring this up through a no-win, no-fee solicitor? Or is there an alternative route I could pursue?