Leaking conservatory floor/wall

[iantresman]

After it rains, our conservatory/lean-to/porch, gets a little water coming in through around the wall/floor. Not much, but nearly the whole outside circumference. As tenants, we don't know how it was constructed.
The outside photo shows an "indent" at floor level (above ground level) which I suspect is collecting the water. The appears to be some sealant inside, so I'm wondering whether filling in the indent with sealant would help,or some kind of plastic "flashing"?

Indoor

conservatory inside 1200.jpg (141.34 KiB) Viewed 6836 times

Outdoor

conservatory outside 1200.jpg (126.25 KiB) Viewed 6836 times