Don't pay until you have asked.
Why isn’t the warranty picking up the bill?
What was the actual cause of the miss-fire according to the garage?
Why did each of the parts need changing and where are the parts they took off your car, all of them.
Who did they give the estimate/quote to before starting.
Who gave them authority to start the work.
Lots of garages get you to sign a box allowing them to do work up to a certain ammount before having to call you again.
Get them to put everything in writing, the cause of the fault, why the warranty company won't cover it, on who's authority they started the work, the reason why each of the spare parts was needed. Be very insistant, tell them if its not in writing there is no way your going to even consider paying.
Assuming everything is as you say it is, then they are trying it on; they probably started the work before getting approval from the warranty company, who latter said no, so they are coming after you.
Depending on how it goes say you won't pay and ask them to put the car back to how it was before you took it in.
They will try to negotiate out of it, see what they offer, get back on the forum.
Finally if you don't like they're offer pay a solicitor to send them a letter.
Bottom line don't pay for any work you didn't approve or are unhappy with.