Sorry to hear about the school troubles. Maybe you just need a "better" school rather than one with a particularly good way with "dyslexia".
What are the literacy difficulties your child is experiencing, and to what degree? Are you both working full-time, or do you have some time to do some appropriate tuition at home yourselves?
It's generally (but not always) the case that children in the early stages of learning to read, write and spell will make significant improvement with a systematic phonics programme that teaches reading, writing and spelling. Also a focus on handwriting is quite often needed.
To what extent can your son read and write, and what method(s) has he been taught by so far?
What did the Educational Psychologist suggest was necessary to produce good gains in his literacy learning? Some are good at this, others really just focus on the "diagnosis" (a controversial one it would seem). Can you do any of it at home?
Have you read the recent threads on this section about Toe by Toe etc?
There are also quite a few ipad apps these days that help a child learn to read by phonics. You will find a whole thread devoted to it on the rrf website. Also try the website mentioned in another thread on here ........ I think it was www.dyslexics.org.uk
There is no particular evidence that there is a subset of children with "reading difficulties" who have "dyslexia", and the effective methods for improving reading, spelling etc etc work just as well on children with "dyslexia" as on the rest of the population of children with "reading difficulties" or "literacy difficulties".
So if you do look for a different state primary school you might prefer not to focus on "dyslexia" as such but how they would do a systematic, and strongly phonics based "catch-up" with your son. Another route in to choosing a new school, if you really need to, might be to find out about some programmes that get good results (e.g. Sounds-Write, Read Write Inc) etc etc and then see if you can contact the programme authors to find out schools in the area(s) you are interested in who currently get good results with those prgorammes. You would then still need to see if that school suited your son in other ways, and how they would deal with a "catch-up" situation.
Even if you have a school that is really experienced in this or a private tutor worth their salt, it's going to take some well-focused daily work at home to effect a catch-up. Even with the right support, it takes a while to get improvement. With at least 30 mins a day of effective one to one or small group work, either at school or at home, you should start to have noticeable improvement and a gain in self-esteem quite early on.