Most likely it's the bearings. If you're a competent DIYer and have the time and inclination you could probably manage to replace them yourself but it will be a git to do, especially if you are on your own.
The drum will almost certainly need to come out, and that is likely to mean dismantling much of the machine.
If you are careful (UNPLUG FIRST!)and have a decent set of tools it should be possible but for a first timer you'll at least need a full day, and if you hit a problem it could be longer.
The trickiest bit will be drifting out the existing bearing, and installing the replacement without damaging the bearing, drum or "spider" (thats the bit that is attached to the rear of the inner drum). That will mean finding some heavy gauge pipe (or similar)of the same or slightly smaller diameter (width) as the bearings. You then put the pipe carefully against the bearing and carefully wack (the pipe) with a mallet until it comes free, making sure the pipe and the angle it is struck at is exactly 90 degrees to the bearing surface. If you managed to remove the drum you might get a friendly local garage to do it for you for 30 mins labour. Fitting the replacement bearings (there are usually two sets) often means dropping them in a freezer for a while, and/or heating the drum around where the bearings seat. This gives a bit more clearance when positioning the new bearings and avoids the need to wack them too hard (saving possible damage)
The parts will be easy enough to get hold of and are likely to be pretty cheap (I'd guess around GB£30).
Have a look at the washing machine forum on ukwhitegoods.co.uk which is a good place to ask for advice on your particular machine - make sure you have the model number off the machine label as they will want that. I had an FL1032 Zanussi and it was great - ran for years with maximum daily punishment.
To sum up, only consider doing this if you are either handy with a spanner and have plenty of time so you won't be rushed (not likely I grant you), and there isn't something else that is going wrong. Don't bother buying a new cheapy machine as it is sure to be crummy and break in no time.
Otherwise buy a s/h Miele off ebay. Pay around GB100 and you'll have a machine that will last ages and always be worth repairing.
Whatever you decide to do, good luck!
Adrian, April 2008