My ds has struggled with anxiety for as long as I can remember, we have spells when it's better and spells when it's horrific. Some things which have helped:
Environmental changes - sensory and social overload are pretty standard for autistic people, finding ways to reduce this, knowing what raises anxiety and addressing this, avoiding places which make things worse, all help. Keeping a diary do you spot patterns helps. Has your ds been assessed by an OT as part of his assessment/does he have an OT?
Scaffolding - my ds needs the familiarity of a routine, which gives him a sort of scaffolding for every day, he's less anxious when he knows what to expect and is well prepared for changes. He tends to cope better with huge change than small!
CBT - I've used Dawn Huebner's 'What to do ... ' CBT workbooks (Amazon have them) to great effect, they are short structured CBT programmes in workbook form you work through and implement yourselves.
I really rate Ross Greene's book 'The Explosive Child', it's more than the title suggests and is an excellent foundation for parenting highly anxious children.
'The Incredible 5 Point' scale is another good resource for emotion stuff.
The Huebner books you'll need paper copies as they are workbooks with activities.
It takes time and a lot of trial and error to work out what works.
Are you going to request NHS assessment too? Ideally autism assessment should be multi-disciplinary and include speech and language and an OT assessment. You could ask for referrals through your GP.
Is he well supported at school?
Don't worry about surprises, part of parenting an autistic child is working out what works for them, and if he doesn't like surprises, don't do them! Give him the sort of great day he will enjoy not what convention says he should enjoy
Do you think it is worth me getting the NHS to assess him also? The school are doing their best to support him, but he does need a lot more they can not offer 1-1 I have looked at another school online but it is a bit far away from where we live.
I think it would be worth seeing your GP and asking for a full assessment as per NICE guidelines. This will get ds in 'the system' and generally NHS diagnoses are better respected in the education system, which at the moment, while he's a child, is most important.
Did the psych talk about what next, local services, courses for parents of newly diagnosed children, what you/ds might be entitled to sort of things? I'm not suggesting there's a raft of help after an NHS diagnosis but generally you have some access to something!