A 1970s rear extension with a felt roof that had been patched three times. Water was standing on it for days after rain, which told us the problem was the fall and not the covering.
Lifting the felt showed a soft chipboard deck and no fall at all. We took it back to the joists, laid a new 18mm ply deck firred to a proper fall, and covered it in a single piece of EPDM with no field seams. Powder-coated aluminium trims and a new outlet into the existing downpipe.
Two days on site. The roof drains dry within an hour of the rain stopping.