If you have had work carried out which was not of satisfactory quality, you need to make sure this is the case, according to the new owner, you first need from the new owner the proof that the work is unsatisfactory. As BM says the new owner having the work done again without reference to you has not helped your legal position. The correct course of action would have been, if you were satisfied that the work was not of satisfactory quality, which is one of your statutory rights, to go back to the original person, with whom you had a contract and ask him to complete the work to a satisfactory standard within, say two weeks, at the agreed cost. Only if he failed to do so or ignored you should you have the work done by others to a satisfactory standard and charge the original person with any cost. In the event of him refusing to pay you would need to take action in the county court.
I suggest you explain the legal position to the new owner and explain how his actions have not helped, if he wishes you to take action against the original person, (with whom you had a contract) you will do so at his (the new owners) risk and cost. There will be costs involved in you taking action in the county court and you may lose.