If it is 7 am and the hotel does not allow you to check in, you still have many options to do such as Breakfast, sightseeing, spa(if opens) or just walking.
However, if it is 2am and the hotel does not allow you, what can you do?
If the walk in rate is reasonable, you might just pay for it.
But if no standard room is available or the hotel charges you much higher rate, you have to pay the high price or sleep at lobby lounge(not recommended).
Anyway, it seems to be risky if you try to check in 2am without the night reservation.

If you arrive at LHR around midnight, there are cheaper SPG hotels near airport so you could just stay there overnight, and in the morning, you can move to Sheraton Park tower.