It's a petrol engine.

They have been very good so far but I am just trying to understand where I am from a legal point of view. I don't really want to wait for a dispute between the garage and supplier to be resolved, that could go on forever!

Your contract is with the garage. They supplied the parts and the labour.

Whether it is a failure of a part or failure to installation is relevant to the garage as to who pays - themselves or the part manufacturer is irrelevant to you

As your contract is with the garage they have to to fix the problem - (

1) repair your engine or

(2) fit a re-conditioned (2nd hand) or

(3) pay out the value of your car if 1&2 exceed the value of your car.

Exactly - imagine that the parts supplier disputes liability, saying that it was the mechanic's fault. According to the garage's view, you would have to wait until that was resolved before your car is repaired. It is good though that the garage has blamed it on faulty goods they supplied - as a consumer that gives you a clear right to be put back into the position before it failed.

Might be worth getting an independent inspection if the garage and supplier are going to bat the ball (you) between themselves to absolve blame.

If you don't know the garage they could do anything while they have the car to push the blame away from themselves - especially if its negligence on their part.

It's time to get a solicitor involved to remind the garage that they are responsible for the failure of the engine, as a result of their faulty work whatever the cause, and to agree a time scale for the repair.

It's up to the garage to take legal action against their supplier of the parts if they can, to recover their cost of repairing the OP's engine. That is nothing to do with the OP.