Badgers are indeed protected and have been since 1973. Protection of their setts did not come until 1991. It is illegal to kill, injure, take or cruelly ill-treat any badger, or to attempt to do any of these things.
Once badgers have a latrine area they do tend to go on using that same spot, though not necessarily continuously. They tend to be creatures of habit. As you say, fencing that area off securely may do the trick.
Sealing off the rubbish bag will probably also help. Badgers tend to return to good foraging areas once they have found them, and if your garden becomes a 'bad' foraging area due to there being nothing to eat there, then hopefully their visits will become much less frequent. I have a feeling that the visits may not stop completely, as your garden must fall within an established territory and so the badgers will doubtless return from time to time to check out the possibilities food-wise. Badger-proof fencing all around the garden is probably the only long-term solution, though this may be an expensive option depending on the size of the garden and on what type of fencing you have already.
Electric fencing can be very effective at deterring badgers. If the garden is large and it would be impractical to erect such fencing all the way round the edge, it would be better to identify access points if possible and erect such fencing in those places. More info on the use of electric fencing to deter badgers can be obtained from a DEFRA leaflet which available online as a PDF file:
http://www.defra.gov.uk/corporate/regulat/forms/cons_man/vertpest/wm15.pdfIt is aimed at farmers but the same principles apply.
Lots of people like having badgers visiting their gardens but I can quite understand those who don't when badgers cause damage, or decide to site their latrines in the garden. It is usually possible to reduce the damage, or even eliminate it, without harming the animals, though sometimes it may take a while to find the right solution for the particular circumstances.
Steve