Re: Simple Question
Another not comletely uncommon common problem is a breakage in the cable itself: If your measurement includes a flexible cable from the plug, and it is aa old one 8already used for a longer time) there might be a breakag of copper inside the isolation - typically in a place where it is bent most, such as close to the plug. I have often cut off about 5 cm from the plug end of the cable, and re-terminated to the plug in those cases.
I am not completely familiar with the UK plugs, but isn't there a fuse as well? It should be in series with the "L" line, and if it is gone or missing, you have no connectivity.
And I want to repeat what oldeboots already said, because i is so important: Be careful with mains wiring - there are both shock and fire hazards!
Good luck!