There is no legal requirement for a quote per se. Whatever way you can come to an agreement is fine.
I had an accident many years ago and I sent a letter to the at-fault driver demanding that they pay to repair or replace the car, and I did not specify an amount. The other driver passed it on to their insurance company, the insurance company had the damage assessed and then they made me a cash offer which I accepted.
If the cost is in dispute then you can get a quote as evidence that they are not offering enough money.
