I've got a fairly large (4m by 3m) brick built garden 'shed' which has
a tiled roof. The slope on the roof is very shallow, so much so that
the tiles are practically horizontal.

The roof of the shed is now leaking (its been up there for maybe 15
years). The tiles look fine, so it looks like the leak is due to the
very shallow slope which doesn't allow the rain to run off properly.
There is a plastic sheet under the tiles, which has gone brittle,
which is where the water is probably getting in.

The question is which of the following options should I go for to
repair the roof:

1) Remove the tiles and battons underneath and replace the plastic
sheet above the rafters with a new one and then re-tile.

2) Replace the tiled roof with a felt or fibreglass roof.

Any opinions and does anyone have experience of fibreglass roofs?