Allow yourself about five hours. The easy bit is up the M1 / M6 to Stoke-on-Trent, but what they don't tell you is tha Alton Towers is sited in a country village, miles from anywhere. the access is one country road, which gets really jammed, so aim to be arriving at the Towers around 9.30 a.m. on the morning of your visit, to avoid the worst of the crush - compounded by dozens of large coaches which jame the road even more. it is worth the trek though - have a good time.
Central London to Stafford Takes 2.5 Hours (using the M6 toll) Stafford to Alton Towers takes 30 mins. I would therefore venture 3 hours assuming you do not have to stop more than once.
It does depend upon where in the big smoke you are starting. Once on the M1 I it will take about 2hrs from the M25. I will suggest that you stay away from the M6 and stay on the M1 until jct24. Follow the signs on the A50 to Uttox�er then to the towers. If you use the M6 this means you will be joining the A500. Loads of road works + it is longer. Enjoy