My DS has just been diagnosed, it took just under a year from initial concerns to getting dx.
Note that each borough uses different pathways, but this was my experience:
Teacher raised concerns that coincided with my own. Went to GP and asked for referral to community paediatrics. He suggested school also refer and see which was fastest,
School made referrals to occupational Health, educational psychologist and speech and language and also got school nurse involved to help with his anxiety.
During this time I read all I could. Go to the national autistic society website and read their guides. Tony Atwood books on Aspergers is particularly helpful.
OT and SALT were really helpful, not everyone has the same experience though. They picked up on sensory processing issues, hypermobility and social communication / interaction difficulties. They also made numerous recommendations that the school could do to aid comprehension and learning, even without diagnosis.
Comm paed carried out physical examination and a 2 hour session going through the DSM V criteria for autism. There was also numerous strength & difficulty questionnaires and observation forms.
EP met with me to discuss DS and observed in school. DS now has 3 monthly reviews.
All reports went to a panel for review, DS was given dx end of October.
My advice would be to educate yourself as much as possible. be prepared to battle as not all will be willing to see what you see. Try ASD learning strategies and if they work then all the better. And remember it's called autistic spectrum disorder, so you may not tick every box and that's fine - your DS will have areas of strength as well as difficulties, focus on the positive as well.