'Builder' continues to be used by the general public in the UK to describe any sort of contractor on a building site but 'proper' builders in this area are mostly time-served tradespeople who don't expect free cups of tea (although to keep you happy they might accept one - it's your time after all :)

In domestic work your 'builder' may well be from another trade - a Joiner is quite normal - or not a tradesperson at all - just someone who has set up a building firm. Unfortunately there is no requirement to have a qualification (but it seems to me under the CDM 2015 Health & Safety Regulations which now apply to all construction work in the UK, anyone calling themselves by a trade name such as 'builder', is certifying that they are competent to fulfil that role - but we will see how that turns out).

...'and he fell among plumbers' was a phrase one old builder was fond of using hereabouts which was always amusing.

A plumber (from the Latin word for lead, plumbum) is often a heating engineer as well. Even on domestic scale jobs a good plumber/heating engineer can make a huge difference to the effectiveness of the heating and hot and cold water systems.