Can any solicitor write a pre-action letter or bring a JR claim?

In theory yes, but in practice you would be much better advised to go to solicitors with experience in education and/or public law, ideally with a legal aid contract. We have seen some poor quality pre-action letters from solicitors or self-styled legal advisers/SEN advisers which were simply a waste of time and money. Details of solicitors with the relevant contracts can be obtained from the Legal Aid Agency.