Might be worth adding here that at some UK airports (Heathrow, Gatwick and Manchester only I believe but ready to stand corrected) you can also be 'cleared to land after' - which differs from the MATS 1 version.
For example: 'xxx123 after the landed/vacating 737 CLEARED to land runway 27L'.
This is a provision of separation from the controller and can only be given if when the aircraft issued the clearance crosses the threshold the subject aircraft will have vacated the runway or if still on the runway will be 2500m from the threshold.