I am replacing a pendant light together with the light switch. I've
totally disconnected them from the mains wiring -- I basically have two
sets of three wires sticking out of the wall and out of the ceiling.

When I turn the power back on at the consumer unit, and use a mains
tester (screwdriver type) on the three wires sticking out of the
ceiling, all three are shown as LIVE.

This strikes me as very odd.

Is this necessarily indicative of a serious wiring problem somewhere?

Thanks
Alexei