It's a minimum of 120 seconds (must be in a Nats AIC somewhere) and, yes, the controller estimates the time to roll and rotate but its not rocket science as depending on the type departing anywhere from 25-45 seconds works well.
As wake generation is only considered to start upon rotation thats the time that it's based on. It wouldn't really be the same if you waited two minutes from the commencement of roll due to the take-off runs required for different types/destinations. Eg. a B773 to South America will need a lot more Rwy than a B77f with a light load going to Europe. With the known rotation time you have one less variable to consider and it's easier to be more accurate.