Now here's something which has been the topic of hot debate recently at units...
First of all, taking an arrival following a departure:
Gatwick and Stansted can still use the 'after the departing cleared to land' procedure after a comprehensive safety case was put forward for it's use in high intensity single runway operations.
The separations for this procedure are as follows:
Once the landing aircraft passes above the landing threshold ('the keys') the departing aircraft will either be airborne and 2000m along the runway, or not airborne and 2500m along the runway. This in theory allows a departing aircraft to still be on the runway when an arrival touches down - but taking Gatwick's runway as an example the displaced threshold and overall length renders this virtually impossible. Certainly 10-15 seconds is perfectly reasonable and easily achieved whilst meeting these requirements.
Heathrow and Manchester both withdrew this procedure.
To issue a standard landing clearance MATS 1 procedures state that an aircraft should be issued with a landing clearance before it is overhead the runway. After much discussion, including SRG, the runway is confirmed as the departure and the landing runway and hence in this case it is not the landing threshold but the start of the starter strip that the aircraft should receive it's clearance before. In this case, it's still perfectly possible to have approximately 15 secs between a departure rotating and an arrival touching down, but less likely.
For an arrival following an arrival:
All airports can still use the standard MATS 1 'land after' procedure, for which there is no standard separation to my knowledge. This procedure essentially puts the requirement for separation in the hands of the pilots, indicated by the ominous omission of the word 'clear' in any tense. In this case, if all parties are happy then there may well be two landing aircraft touching the runway at the same time - albeit virtually at the opposite ends. This 'concept' is just as valid at major airports as at a local airfield. Of course, controllers and pilots use their skill and judgement to decide what is reasonable, and the distances involved are vastly increased to take the speed, weight and manoeuvreability of the aircraft into account.
Also at Gatwick and Stansted there is the opportunity to issue a 'after the landing/landed/vacating cleared to land' which works in a similar way to the other clearances above. In this situation the controller is ensuring that the first arrival will have vacated the runway by the time the second crosses overhead the landing threshold.
I'm not sure if Heathrow and Manchester can still do this, but presumably they can.
Phew. If you're still here and not an ATCO or pilot, well done, you really are an enthusiast...
To sum up:
A 'land after' following another arrival is prefectly acceptable at all airports and is issued at Heathrow and Gatwick quite frequently. I'm surprised that Luton and Stansted use this less.
If you receive a 'late landing clearance' at whatever distance, against a departure or arrival ahead, this should be received before your aircraft is overhead the physical concrete/asphalt of the runway.
At Gatwick and Stansted you may also receive an 'after the departing cleared to land' clearance which ensures the specified separation given above.