Given the dispute with a council, there is an Ombudsman scheme first of all, which definitely needs to be explored first. It is free to use and may resolve this without you having to use a solicitor and pursue court action.
You should first make a complaint to the council here: https://www.complaintsdepartment.co.uk/richmond-upon-thames-council/ and if that does not resolve this, involve the Local Government Ombudsman (LGO) : www.lgo.org.uk/make-a-complaint
The LGO may be able to help but you would need to firstly exhaust the council's complaints procedure, unless you have done this already. The Ombudsman scheme is free of charge and quicker than court action. As it is an arbitration scheme, the Ombudsman’s decision would be binding upon the council if you accepted the decision.
If the Ombudsman does not uphold your complaint, or you disagree with their decision then there is a legal remedy available against a council with it being a public body.
You can issue "Judicial Review" proceedings which is where you involve the court, and a senior judge or panel of judges looks at the legality of a council's decision. If the judge(s) find in your favour, they will make an order which is binding on the public body (e.g. they may say the public body’s decision was invalid or indeed illegal) and they are then forced to act to sort the problem out. Further, if your human rights were breached then compensation may also be payable.
The issue with judicial review is that the cases are quite complex, but as a result of that, a law firm can usually recover their legal costs from the council if they win the application. You should be able to have a no win no fee agreement with the law firm, to sue the council. Or if you are in receipt of means tested benefits then legal aid may well be available to you.
Here are a few firms who specialise in this area :
If the above say they cannot help then there are pro bono (free of charge) lawyers who could assist you. You can try these firms for legal representation (they are a charity who connect you to pro bono lawyers) : LawWorks or /www.nationalprobonocentre.org.uk/finding-legal-help/
Here is another: https://www.lawcentres.org.uk
And there is this one : Advocate: Finding free legal help from barristers