What if there are no buses, especially at the times he might need them?
I don't know if you're just being obtuse, but the OP has chosen to buy a car in a way that *should* be absolutely minimal risk of something going wrong, and if it does, you've paid the premium to have it fixed and the impact to your life minimal. We all accept that the more you cheap out, the more hassle it'll likely be to get something repaired or replaced - some are happy to take on this hassle because they have the time, means or skills for it not to be an issue. The OP obviously doesn't have this luxury, so he has correctly chosen to buy in a way that is supposed to be the pinnacle of the buying and owning experience.
If he had bought a £500 banger from Dodgy Dave down the road - then yes, the bus/train/taxi/hiring his own car should be something which he should absolutely expect to have to do. But if you've bought a brand new £40k(?) car from a main dealer, with the main dealer warranty - you shouldn't have to even start thinking about this stuff.
No, but you CAN expect a business to be run in such a way that a customer, who has bought their car from you in good faith, can have their car fixed under warranty in a timely manner. The OP said some dealers were quoting nearly 2 months until they can book it in just for diagnosis - which tells me there is a colossal failure in some area of their business. In no one's book is this even remotely acceptable.
Completely invalid argument. There is no expectation for said "good builder" to take on your job in a timely manner. You owe him nothing and he owes you nothing.