The distance to Central London from Bath is about 115 miles and is very difficult to gauge the journey time. Time to get to the outskirts of London can be 1 hour 45 minutes, but depending on the area of London can take just as long or even longer for the last 15 to 20 miles.
London has very bad traffic problems. Also, if you travel to Central London, there is the London Congestion Zone. This operates all day, every day and the charge to enter is £15 per day.
As London covers a large area, quotes are based on the area of London you are travelling to or from.