With this in mind, if ‘simultaneous parallel approaches/take-off’s’ were to be introduced at LHR, would this increase the number of ‘slots’ because in effect you are having two aircraft taking off quicker than at present by using just one runway for take-off’s and the other for landings, or is it not as simple as I am thinking?

You’re really getting into Mixed Mode there, and that’s a whole new can of worms. To do parallel departures, you need decent weather, of course, and you can only do it with a/c on diverging tracks….I’ve done it a few times late at night and during the only quiet day of the year, Christmas day. It’s a bit dangerous to have a southbound rolling off 27R the same time as a northbound off 27L.

Mixed mode will increase the runway movement rates by about 10-15%, but because the airfield is short of stands, it will not mean, at least for a few years, any more slots, merely to improve the resilience of the airport in delay situations.

Mixed mode is horrifying to see on GMC, though.