Type in London for start position, Alton Towers for end position - make sure shortest time is ticked and it should come up with 2 hrs 29 mins (151.2 miles).
I would say that 2 hours 29 minutes was optimistic and nearer 3 hours (without a break) is more likely.
That is from Central London, it may be less if you are already in North London. May be more if you are going in the rush hour.
The problem is that Alton Towers is in the middle of nowhere (to be honest it is the WORST place to put a theme park) and although the journey is mostly M1 motorway, once you turn off the motorway you are on very small local roads that will really slow you down.
Not sure why you are asking about Alton Towers but if you are in London you are better going to Thorpe Park or Chessington World of Adventures.