Dodo,
Not sure where you are based, but we found an excellent product in Nolan's Hardware in Clontarf. I think it's called 'Drain Clear' (it has 'The Plumber's choice' written on the side and is in a opaque bottle with an orange label. We use this regularly. Pour and leave to stand for 15 mins and run through loads of water.
When you pour it, smoke-like stuff will come up the plughole, depending on how much hair,etc there is. Open all the windows as the smell of burning can be very strong. Is an excellent product and the only one that works for us - we tried lots of products. We have moved house a number of times in the past 4 years so had to clear a lot of plugholes! We never found it anywhere else only in Nolans. Costs about €8
HTH
D