Garage costs for not repairing car

I recently broke down in my Chrysler 300c and the car was towed to a national chain garage, Mr Clutch, who are RAC approved, trading standards approved and advertise their expertise on Chrysler.

The breakdown was an engine management light on and running in limp mode. Asked the garage to find the problem and fix the issue. thy advised the fault on the diagnostics was " multiple misfires", so they changed the spark plugs, ht leads and the coil. None of this resolved the issue and the car is the same as when I took it in. They have advised me that they can't work out what the cause of the problem is so I need to take the car somewhere else where they might be able to help.

Mr Clutch have stated that they followed recognised course of diagnostics and parts replacement in an attempt to resolve the issue and therefore they require me to pay £600 costs before I can take the car to another garage.

What's my legal position? if they charged me for diagnostics time I could understand it, but for replacement parts that didn't resolve the issue and therefore potentially didn't need replacing, I do object.

anyone have any advise?