How long does it take to tour westminster abbey?

It takes as long as you want it to take. It's stuffed full of memorials and monuments, though, so if you're interested in that kind of thing I'd allow at least an hour or two to do the place justice. To give you an idea, a tour led by a verger takes 90 minutes, or you can get an audio handset like a Walkman or iPod free with your entry ticket and to follow that in full takes about an hour.