It is a provision of the Supply of Goods and Services Act which applies to contracts entered into before October 2015, that a job is carried out with reasonable care and skill and is as described.
If the service should have included a change of transmission fluid then they have failed to do that and hence they are in breach.
As a result of the breach, you may have suffered loss.
You are going to need a report from an independent engineer which confirms that the failure is as a result of the change of transmission fluid.
It’s not unreasonable to let the original garage effect the repair but I can understand in circumstances like this why you don’t want them to do it.
You don’t give them the opportunity to inspect the gearbox, they can allege that it was a completely different problem and hence, whilst you may not want them to do this, it is going to be a wise move to allow them to look at it.
Unless you can get the engineers report which is unequivocal in its opinion that this failure was caused by the non-changing of the fluid, then your claim will fail.
Can I clarify anything else for you?
Please rate the service positive. It doesn’t cost you anything but helps me greatly.
We can still exchange emails. Best wishes. FES.