To the OP, as you can see, there are many answers depending on one's perspective. To answer the question correctly it's important to know exactly what you are asking - and that's not intended to sound flippant. Separation is what controllers need between aircraft - in the books there are lots of different separations, and the name of the game for the controller is to have one of those separations between all of the aircraft at all times.
In a radar environment such as Heathrow, the easiest separation is 5 (or sometimes 3) between targets laterally or 1000 ft vertically. The MDI system - which takes account of the route and average speed of the class of aircraft - is designed to deliver aircraft to the radar controller, when they appear on radar, with that lateral separation minimum in place. At places without an MDI system there are other time-based separations like the two minutes that HD mentions - IIRC this would be the minimum separation for two aircraft on the same route if the first is 40kts or more faster than the second.
A tower controller also has to consider wake turbulence separation, which has become more complicated than it was when I was an operational controller - but would require two minutes for a Heavy followed by a Medium from the same point on the runway. I don't think any wake turbulence separation is required between two Mediums (but I stand to be corrected by someone who is doing it as the day job) so for the example you use it would be determined by whatever the MDI table says or when the pressure is on, whenever the receiving controller says its OK to launch the next one. I've never worked Heathrow but at my last operational unit when it was busy it was quite common for the approach controller to turn one off the SID on first contact which enabled the next to be launched maybe a minute later. If it was good wx and the tower controller could do visual separation from the VCR the second could be cleared to go when the wheels of the first left the ground if there were no other constraints.