I am unsure if I should rely on this overdraft extension being there in a few days?
In theory any overdraft facility may be withdrawn at any time. Having said that, unlike PayDay lenders, banks do follow certain rules and protocols. If they do withdraw the facility they should give you a few weeks notice. You should print off evidence that the overdraft is authorised, use it to clear the payday loan and pay the overdraft off on pay day.
Another time, in a similar situation, you should ask the garage if you can pay after a week. They are making money out of you and will often help in a situation like this, particularly if you have been a customer before. Some garages will take post-dated cheques but you need to trust/agree that they wont pay them in early. Other garages will take half now, half in a couple of weeks. Some garages wont let you take the car until the work has been paid for. It's best to agree when, how and how much you'll pay before they start the work.
Better still, anyone who relies on a vehicle should keep a few hundred pounds ready for any emergency. Personally I always try to make sure that I can find £500 as that is enough to buy a car that works.