Yes, the waiting lists are very, very long. I used to work in a job adjacent to dealing with complaints about the NHS, some about delays in referrals to gender services, and the outcome of complaints was generally, "it's not great but the NHS can't refer you to specialists that don't exist".It's not quite like that - as Hannah Barnes explains in A Time to Think, what's been happening for families using NHS services in England, if the child is seen as having gender issues, the treatment path is referral to the specialist gender service (that was the Tavistock) with very long waiting lists, even if there are other known issues (like autism) the gender identity issues trump them. There was a high possibility that eventually the child would be referred for puberty blockers - but it wouldn't happen quickly, as the numbers of referrals were growing so quickly. This is where services like Gender GP would come in to sell puberty blockers to families frustrated by the long delays - but they're operating outside the NHS.
TRAs will have you believe it's transphobia or under-funding, but you can't magic specialist doctors who want to do this sort of work out of thin air. There just aren't that many of them. It's a niche area, as it should be, and the fact services are cluttered up with confused teenagers who have had their social contagion mindlessly affirmed by useful idiots isn't the fault of the NHS.
The fact that any autistic children (or those with other co-morbidities with gender/identity questioning) have been funnelled away from proper diagnosed and treatment and into services that affirm the idea they're the opposite sex should be a medical scandal.