I have not gone into a detailed investigation of these trains, but either a steam-powered pump was fixed to the engine or more commonly one or more portable pumps were carried on the train. These pumps, in common with all Fire Service pumps, have a 'suction hose' which takes water from the source into the pump where it is pressurised and discharged into fire-fighting hose via outlet(s) on the pump. The pumps were equipped with 'Primers' which could generate a a vacuum in the suction side of the pump to lift water from a source below the level of the pump.
However, with fire trains, the pumps were usually below the level of the water in the tanks (often old engine tenders). The tanks would be linked together to allow pump(s) to run without interruption.
I used to be a member of the Fire Brigade Society - see
www.thefirebrigadesociety.co.uk and it may be worth contacting them; I don't recall such trains being mentioned in their Journal while I was a member.
There is a photo in "Britain's Railways at War" by Alan Earnshore (Atlantic Transport Publishers, 1995) which shows how in WW2 portable 'trailer' pumps were carried in covered vans fitted with built-in hoists so the pumps could quickly lifted out to be wheeled to wherever they were needed.