1. Make sure that you can justify each element of the total sum you're claiming. (i.e. rather than simply saying "You owe me £x", you need to be able to say "You owe me £y for these materials, £z for these materials, £a for the remedial work done by guy A and £b for the work done by guy B", together with having receipts available).
2. Prepare a formal written demand to the plumber. Your letter must include:
(a) your name and address ;
(b) his name and address (NB: If he's trading as a limited company, it should be the company name, and not that of the plumber, shown on your demand) ;
(c) the date ;
(d) the words 'Demand for payment' ;
(e) the total amount demanded ;
(f) the reason why you believe you have the right to receive that sum (e.g. "in order to remedy your poor workmanship, I have had to make the following payments") ;
(g) a clear statement that, if payment is not received within a given period (I suggest 14 days), you will commence legal proceedings ;
(h) a further statement that, if court action becomes necessary, you will ask the court to add your legal expenses to the CCJ that is made against him ;
(i) your signature.
3. Send your demand to the plumber using Royal Mail's 'Signed For' service. (Do that even if he lives next door to you and you could easily pop it through his letterbox. You might need to convince a court that he actually received the demand).
4. Wait to see if he pays you within the period specified in your letter.
5. If you don't get payment, commence legal proceedings via HM Courts and Tribunals Service's online system:
https://www.moneyclaim.gov.uk/web/mcol/welcome