Welcome to the forum...
a standard multi-meter isn't really the best thing for checking if a cable is live..
and within the electrical industry it is not a recognised tool for proving if a circuit is live or dead..
Some of the problem is that a multi-meter requires a good battery, a working LCD display, and two probes with a good connection onto two points, to be able to read a voltage..
Plus if both of those wires were live, the meter would show 0volts and not give any warning..
Whereas an approved voltage tester will be able to give some sort or warning, (typically audible), with just a single probe connected onto a live wire..
and with both probes connected can generally show either an approx voltage range or the exact voltage if it includes an LCD display.
e.g.
https://www.screwfix.com/p/di-log-combivolt-1-ac-dc-2-pole-voltage-continuity-tester-led-690v/371jp
https://www.toolstation.com/tis-851-voltage-continuity-tester-self-proving/p51437
https://www.tlc-direct.co.uk/Products/TMDL6780.html
They cost a bit more..
But these type of devices do NOT need good working batteries to detect a mains voltage on a cable..
i.e.
one of the specs quote:
"Features fully operational voltage indication even when batteries are discharged."
And if you get it wrong electricity can kill a healthy adult in less than a second..
so a few more pounds can be a worthwhile investment..
some are into the £100+ range..
but for less than £50 a reasonable voltage tester can be purchased..
just google "Voltage Tester" to see if you can find any similar looking tools cheaper..
(obviously some sites need VAT & delivery added.. so the Screwfix price may not seem quite so expensive..
Also if it does go faulty any outlet with a physical store local to you can save a load of hassle)..
p.s. IMHO Multi-meters are general best for hobby electronics, or auto electrics, not the first choice for mains wiring.
hope that helps..
Guinness