Lead gutter gully has lost half of it's fall

[Welikejazz]

This lead gutter takes rainwater from the lead lined roof of the flat below ours. It is below our suspended roof terrace. Over the years it has lost approximately half of it's fall, and standing water sits every time it rains, or plant containers above are watered. Is there anything can be done to reinstate the fall? There is only one outlet. The standing water does not reach the other, hidden end, so another outlet would not obviously help. Advice much appreciated

 

[oldbutnotdead]

First thing would be to make sure there isn't a dead pigeon blocking the outlet from that gulley (the right-hand end, looking at the pics the gulley is still falling but the water is pooling excessively. Unless the problem bit is out of shot....)
After that, the owners of the flat below have got big problems if their ceiling has moved that much.....

 

[Welikejazz]

No dead pigeon, there's only a small area at the right hand end, covered by the fire escape platform, and I keep it scrupulously clear. The ceiling does not appear to have moved in the flat below, nor water leaked, and our terrace and fire escape show no signs of subsidence either. Only the gulley will only drain from half way along the channel. Is there any way of putting in a ramp at the pooling end?

 

[oldbutnotdead]

No dead pigeon, there's only a small area at the right hand end, covered by the fire escape platform, and I keep it scrupulously clear. The ceiling does not appear to have moved in the flat below, nor water leaked, and our terrace and fire escape show no signs of subsidence either. Only the gulley will only drain from half way along the channel. Is there any way of putting in a ramp at the pooling end?

Could do with a pic of under the fire escape. Either the gulley starts going uphill or the outlet has ridden up.
If the ponding isn't so deep that it's getting into the room below then I'd leave it alone. If water is getting into the flat below its kind of their problem

 

[datarebal]

have a close look and see if the gutter is humped up due to expansion. I can see you have neoprene joints to help prevent issues but it has limitations.
you might be able to dress it down flat if that's the case