de facto & lgw vulture
There is no restriction for a medium following a medium for T/O. On a high density runway like LGW/LHR take off clearance will be given and accepted as soon as the preceding aircrafts nose wheel has lifted. Perfectly normal and happens every day, to criticise the airline shows a lack of knowledge.
For landing the normal spacing is 2.5nm behind a medium and 5nm behind a heavy. LHR has recently switched to time based separation so the spacing can be reduced with strong headwinds, but the time remains constant.