I am not aware of either of these charities providing such a service - Help the Aged do provide a HandyVan service that installs safety equipment for the vulnerable such as smoke detectors and window locks but nothing else.
You can find local Corgi registered gas fitters in the locality here:
http://www.trustcorgi.com/findinstaller/Findan Installer.htmx
And there is HomeServe, a national service
http://www.homeserve.com/
You could also phone your mother's local council and ask if they have a register of approved or recommended gas fitters.
I can't think why a tradesperson would charge pensioners less, to be frank.