Patch up flat roof? Add drains?

[Priyach]

Water seems to be collecting over one side of my flat roof and failing to drain every time it rains (even though gutter on one end is clear). We are looking to replace the roof in long run. Any advice on what can be done to fix the drainage issue in short term? Any cheap solutions to let the water drain from areas in the photo circled in red?
Any re-felting options?
Flats are managed by group of leaseholders like me, so requesting advice please..

 

[jj4091]

Is the hopper or down pipe, that it looks as though it should drain into, blocked

 

[Priyach]

No, that was checked and was not blocked.