On Thursday, 16 August 2018 11:39:18 UTC+1, David WE Roberts (Google) wrote:
The ancient Radiant combi is mounted on an outside wall, and there is a
copper pipe (I assume the condensate drain) sticking out of the wall with
a downwards bend which is more or les constantly dripping.
....
Testing so far not looking good; hot water was working but first test of CH
seems to show that the pump runs, the indicator lights come on, but the
burner doesn't fire up.

Pressure relief valve letting through. Radiator circuit depressurised.

Fill valve may also be letting through, causing the system to go over-pressure, blow off, go under-pressure, etc on a cycle over hours or weeks.

Could also be the diverter valve diaphragm failing to return to rest (CH position).

A quick google suggests these were crap boilers ten years ago :-)

Owain