Freya, first welcome to the board - you've used an (apparently) English term, "tanking" - though I'm not familiar with the term, can I assume it means sealing the basement so it could theoretically act as a tank? I was only in your country for about 6 months clear back in 1967, so only picked up probably 5% of the UK specific slang terms at best -
Basements anywhere are a problem, and I remember enough of English weather to know your location probably isn't too dry below grade. One of the problems with trying to tackle this problem from the inside is that when water can't get where it wants to go, the level tends to rise and the pressure builds up until it either finds a path or MAKES one, which generally makes even MORE of a mess than before. IF you can't eliminate the dampness before building interior walls, you usually only manage to make a non-ventilated place where things can get wetter, mold can grow better, and materials can deteriorate faster
There is an online document I've linked to before, that may help you understand more of the problems and solutions, but I don't think any of the things mentioned could be called "cheap" - it's located here
http://www.buildingscience.com/resource ... ystems.pdf
The problem with this particular situation and soundproofing is that they are almost mutually exclusive - sound proofing requires two masses separated by a hermetically sealed air gap, which should be filled with either fiberglass or rockwool insulation to minimise air currents within the wall - exactly the conditions mold loves, and exactly the conditions you DON'T want if things tend to get damp - instead, you'd want air circulation and heat around the damp area to keep it dry.
When you look at the basement document, you'll see some of the ways builders use to avoid the excess moisture in the first place - however, for an existing construction digging down to below the basement floor (in order to lay proper drainage) from outside is prohibitive for nearly ANY budget.
Since I don't have a basement, I've not kept up with recent offerings in waterproofing coatings, so it's possible there may be something available now that can be coated onto the inside surfaces of a damp basement - you might find better info on this locally by asking a few contractors in your area; if there is such a product, it would have to be pretty expensive in order to be strong enough and adherent enough not to fail under the conditions I mentioned.
It's also possible that others of our members may have knowledge of something that may work for you; hopefully that's true - another thing that I've seen is doing a small well in one corner of a basement and installing an automatic sump pump - however, this wouldn't keep things dry enough by itself to get away with building soundproof walls.
Still others have used dehumidifiers with some success - these aren't cheap, and cost a fair amount per month to run as well, but they do pull a lot of moisture out of the air.
Wish I could be more optimistic, hopefully some of this is helpful... Steve
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