in the letter he does state..."i send a cheque in full and final settlement for work done"
Have a read of this The Law – ‘Full and final settlement’ - Voltimum UK - Electrical Installation Products and Contracting
It would appear that you can cash his cheque and still carry on and continue to sue for the remainder, as long as you inform him at the time of presenting the cheque or a short time after, that you do not accept it as full and final settlement.
HOWEVER I would not take this as proper legal advice. I echo all the other posters who have advised that you seek correct legal advice, BEFORE you make your next move, AND DO NOT present the cheque until you have clarified your position.