Hopefully one of the current ATCOs at Heathrow will provide chapter and verse but there are two types of clearance.
1. "Land after" Where ATC places the responsibility firmly on the pilot to decide whether it is safe.
2. "After the landing cleared to land" where ATC is applying certain criteria to determine that an a/c may land safely. (Of course, the pilot still goes around if he is not happy).
For 2, various conditions have to be met - a/c operating normally, runway dry, by day only and the one ahead must either have landed and be clear of the runway OR at least 2500m down the runway when the next one touches down. I THINK that's roughly the score, but stand to be corrected on the finer points.