A drainage question

We would be very grateful if somebody could help us with any suggestions about what kind of company/contractor could deal with the following problem. The sink and the bathtub in our bathroom (in a downstairs flat in a Victorian terrace) do not drain properly: the water does go away (so the drain is not blocked?), but only quite slowly (although this speed varies for no obvious reason). We have used various strong unblocking substances but this hasn't really helped. When the flat was being renovated before we moved in, our contractor told us he thought that the angle of the pipes was wrong (not enough incline), but this wasn't dealt with. Also, we can now see some signs of leakage at the other (bedroom) side of the wall at which the bathtub is installed in the bathroom. Unfortunately, the bathtub is tiled over, so it's impossible to easily see what is happening. We would be prepared to have the tiles around the bathtub broken if it's clear that this is necessary.