On occasions, tradesmen/women may charge VAT on work completed, but not be VAT registered!
Firstly, by using the VAT number given on their invoice, check here for confirmation of their registration: http://ec.europa.eu/taxationcustoms/vies/vieshome.do
If he/she is VAT registered, and you are also VAT registered, then you may be able to recover all or some of the VAT with a valid VAT invoice as per usual.
If the online search appears to be negative, call HM Revenue & Customs helpline to double check, on 0845 010 9000. Again, if this results in no VAT registration, you will not be able to claim VAT from HMRC. Your claim will be against the tradesperson(s) and a solicitor will then advise you further on the correct action to take. Advice is usually to act quickly as those who are dishonest in the trade tend to disappear without a trace. You should also contact the Office of Fair Trading to prevent this happening again.