Hi, I'm in the UK too. I've ordered from Scarlett's a couple of times and when I emailed for extra information the answer was fast and very friendly.
I'm friends with a vet and she told me that in all her years of training only two days were spent on birds. Not surprising then, that most vets don't have a clue about our pet birds. When I was doing wild bird rescue and rehab the vet used to ring me for advice about pet birds. In the end we worked as a team with the sicker wild birds. She knew about or could research drugs and do stitches while I did everything else. I would say to anyone taking their bird to a non-specialist vet, research beforehand and ask lots of questions. A bird's respiratory system isn't like a mammal's, and anaesthetic therefore carries a greater risk than with mammals. So, personally, I would steer clear of a vet wanting to anaesthetise for such a minor job.
If you're set on having your bird's wings clipped, it's very easy to do yourself. I don't clip my indoor birds, only my ducks who roam around my garden, but even with a small bird it's easier as a two man job. One to hold the bird gently but firmly (if the bird is nervous a cloth loosely laid over the head helps, so they can't see what's going on) and the other person to snip the feathers with a sharp pair of scissors. Look up which feathers to trim before you start (there are bound to be pictures and diagrams if you google), and make sure all the feathers are fully mature - no sheaths around them or blood in them. It's a lot less stressful than a visit to the vet and you can do it at your own pace and to suit your bird's temperament. I hope that helps, and I'm sure there are others on this forum who can give good advice about doing it yourself.