This is a core part of the work of a specialist children's dental service on the NHS. You need to be referred to them - your GDP should be able to do it.
The team I work with (I'm an anaesthetist) will do some stuff under entonox sedation, some with behavioural approaches and some with GA. I only see the GA part of the workload.
Can I just caution that once you are in the system approach what they propose with an open mind - they might not think sedation is the best option.
For my GA work (not just dental) I deal with a lot of kids with autism. I get about 80% of them through their anaesthetic without using pre - GA sedation because I and the team around me have specialist skills at gaining trust/ working with young people with autism.
I appreciate giving a GA tends to be a shorter contact time to managing to complete an entire dental treatment plan but there are similarities - things tend to go awry for me when I can't build rapport with the caregiver e.g if they have a fixed plan in their head and can't/won't engage in a two way dialogue about other options. I might not know your kid but I know what will be asked of them at each point in the process.
Situations where it has gone wrong have worked in both directions - me not managing to give a GA at all after the caregivers flatly rejected me plan for a premed, or me being forced into giving a premed with all the attendant risks when I felt behavioural support would have been more appropriate.
My focus in these situations is to use the time I have to give each child a positive experience that will also help them engage with future healthcare in as straightforward a way as possible.
I had an amazing Mum recently who was understandably anxious as her child has had negative experiences in the past and was really keen to advocate for them. I felt quite strongly that what she wanted wasn't the best option for various reasons (one of which was safety). However, despite this disagreement we had a really productive two way dialogue, and agreed a multi-stage plan together. She then supported me really well in "selling" the plan to her child. In the end option A went really well and I think her child will be much more confident if they find themselves needing hospital care in the future.