Condensation is forming inside the 100mm pipe above the bathroom vent fan which passes through the cold loft (about 10 feet) to a grill at the apex; the water then drips down through the fan when its off. This is in a flat hence the bathroom has no outside walls and also I can't re-route the 100mm pipe horizontally out of the roof.

This is as was fitted from new (1980's) but the first winter for us hence this must happen every day in cold weather when we take a shower.

Any suggestions to stop the condensation forming?

I've even considered fitting some sort of gravity condensate trap which would have to then have a drain pipe leading out through the eaves.

The vent fan comes on when the lights come on so every visit gets the vent fan being used.