My DC are home educated now (previously in state schools - one in special school, the other mainstream).
Some services are a pain in the arse to navigate because the process is to go via the school.
For example, DD was officially diagnosed as autistic aged 10, but I think she's also ADHD. Her paediatrician only diagnoses autism, not ADHD (which is ridiculous anyway - but this is the NHS). The ADHD pathway is different and HAS to go through the school. Apparently the referral won't be accepted or opened until there's a report from the school and the child has to have an EHCP/My Plan+ or equivalent. As a home educated child, there's no school report and no EHCP etc (we had just started the EHCP application when she was in school but didn't pursue it).
I imagine there will be some kind of pathway but it usually takes a whole heap of arguing/persistence. In our experience, referrals are often rejected without the admin person actually looking at the reasons why.
In the battle between state and private schools, home educated kids are often forgotten.
GPs don't often want to help because they think it's up to the school. They get a bit pissed off when there is no school to facilitate referrals. Some things you can refer to directly - like speech and language therapy, and in some areas, OT. Other things need a GP referral, or you have to battle with the provider directly.