Referral has to be through school
For an NHS multi disciplinary assessment, (Paed, Ed Psych, SLT and OT) I think they may mean that to refer to CAMHS or whoever they are outsourcing to because of the huge waitlist, they want two sources of observable different-to-peer behaviour before proceeding , home and school are often the usual ones.
However, it's commonly known by professionals and parents alike that in autism (and some other neurodiverse conditions but autism is the one most often discussed) many children mask at school and are seen as model pupils but they explode on leaving the school premises or arriving at home, whichever they feel able to do.
This vast behavioural difference between school and home is a massive red flag for neurodiversity to be the likely cause and for it to be investigated.
Some GPs and SENCOs are clueless, maybe it's time you asked them both why they don't see that behaviour the same way that any sensible person would
I don't have social media, BUT the advice from many posters in the SN section is along the lines of Do you have Facebook and if so could you look for autism support groups in your local area? They will be very much clued-up on the diagnostic pathway and what you need to do to access it, both via the NHS and privately that will be accepted by the NHS in your area.
Unfortunately, being fobbed-off happens to a lot of us, repeatedly in many cases, but it's essential not to accept that.
It can be a long fight, however with online resources nowadays, there's every chance of success, the only things you need to reinforce are your determination and your knowledge that your child is socially, behaviourally and sensory/emotionally different to their peers and needs support for that.