One is the TrustMark website - www.trustmark.org.uk - where you can search for the trade you need by postcode. TrustMark is a government-endorsed quality mark, and those with it have had their technical skills checked with on-site inspections (their trading record and financial status have also been checked). TrustMark traders agree to a code of practice that covers things like health and safety and customer care, and should be able to offer an insurance-backed warranty, among other things. There’s also a complaints procedure if things go wrong - go to the website to find out more.
Your local trading standards office should also help with finding reputable tradespeople, as many have a register of builders and other contractors, usually recommended by local residents. Those on the register should have been vetted by trading standards and agreed to a code of practice.
Another trading standards scheme is Buy With Confidence. Businesses belonging to it have been vetted and approved by trading standards to make sure they operate legally, honestly and fairly. You can search for local tradespeople on the Buy With Confidence website - www.buywithconfidence.gov.uk.
The online version of getting a recommendation from someone you know is the many reviews-based sites on the web, such as Checkatrade.com, RatedPeople.com and TrustATrader.com.