Yes it is a gravity system, I thought that would be the case when you said it was 30 years old.
It'll probably be a blockage of some sort in the primaries, coil in the tank or heat exchanger, will probably work when the heating is on because the pump is running and it will force it through.
There could be a build of of sludge or limescale, you could drain down and check the condiiton of the primaries, if you're a competent DIYer, if not get a heating engineer out to repair or offer advice.
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