Thank you for your enquiry.
As regards the legal position, if the Vendor agreed to sell the property to you with vacant possession, then they are clearly in breach of Contract if there was someone living there under a rental agreement. I guess that this rental agreement was never disclosed by the Vendors, which they should have done.
Your claim is therefore against the Vendors, and you need to decide whether it is worthwhile pursuing them bearing in mind what you have said about their position.
In order to make a claim, this would normally be done with the assistance of a Solicitor, but if you feel confident enough, you can issue Court proceedings yourself on line- https://www.moneyclaim.gov.uk/
As regards the Estate Agents, although it appears they did a shoddy job, there is no claim agianst them, I'm afraid. At the end of the day, it is the Vendors that were ultimately at fault, and any claim needs to be made against them.
I hope this answers your question, and if so, I would be grateful if you could leave positive feedback.