I get a very annoying clicking noise on my bike (every turn) when I am sitting down on the saddle and pedalling under pressure.

I don’t get the noise when;
I stand up and pedal. Even in the hardest gear, steepest slope.
When I sit down and free wheel over rough ground, smooth ground , fast or slow.
When I am sitting down and in a light gear (1st) and there is little pressure turning the pedals.

So I have to be sitting down. And I have to be pedalling, and pedalling under pressure, which is most of my commute.

The bike shop I use has changed the pedals and also changed the chain and gear case. But the noise still persists.
My bike is fitted with Tannus solid tyres. Over the 2.5 years I have had the bike, two spokes have broken and been replaced.
I cycle roughly 20 miles a week. So nothing too monstrous.

Any ideas ?