I have had a major problem with my car this week meaning it needed a big and expensive repair. After lots of calling round and speaking to different garages I went with one that promised that the repair would be done ASAP. They said that it would be completed bby Saturday or Monday at the very latest. As I need the car for work I went with this . Not the cheapest but the quickest.

However on speaking to the garage yesterday it seems they have not started the repair and when I said I had been promised it would be ready by Monday at the latest the man I was speaking to fell about  laughing and said there was no way it was going to be completed by then. :(  He said he would get the boss who had made the original promises to call me yesterday but of course I haven't heard from him.

My question is when I finally get my car back can I withhold part of the bill because they did not complete the repair when they agreed they would? It doesn't seem to be a problem with the repair itself but the fact that they are just overloaded with work. I was told it didn't go on to the ramps until Friday night as they were busy repairing other cars. they have had my car since wednesday and I was promised work would start immediately.

How annoying !
I would guess - and it is a guess - that it is your word against his if there were no witnesses or you didn't get it in writing.
Sometimes you have to bite the bullet and be nice to them, and appeal to their better nature to get the job done quick. If you go in all guns blazing they could either give it back to you half done and refuse to finish it, or take even longer to finish it