I've only just noticed that this got a bunch more responses. Thanks for the comments and for the support.
I got the car fixed in the end. I called my parents garage (they live 40 minutes away) and asked them about it. They gave me a quote over the phone and arranged to come and collect the car at no additional fee since they had a drop off in that area. They brought it back the next week and that time I had a £10 drop off fee. It all went very smoothly.
I hadn't expected any difficulty about a quote for the work because the damage was to a wing mirror (completely smashed off) so what I needed was cost of new wing mirror + labour. Also, I was only looking for a quote - not a final price. I see other people have different expectations about what garages will do but I was able to find one who would quote me a price and collect the car and their good service means I will always use them in future.
ETA: I thought asking for a quote was reasonable because this is how I've dealt with other work needing to be done. eg calling for a quote for fitting a power shower, repairing a boiler, replacing a broken window etc. In all those cases the tradespeople haven't needed to see the item to quote a cost for the work. That might just be how things work here in the UK but it's been the usual experience of life as a property owner. Unless it's an unusual job or involves multiple elements I'd expect to ask for a quote/estimate sight-unseen for the work.
Whether I was right or wrong about the quote request I think the grown-up comment was very inappropriate and I'm glad I deflected to conversation.
I haven't learnt to drive yet (I had to take a 6 month break as I was finishing a course and needed to concentrate on coursework) but I have moved offices and no longer sit next to my judgemental co-irker!