A friend of mine says that flight data from all airports within the EU are sent to some headquarters in Brussels that process this data (presumably in real time). Ultimately, the permission to take-off or land for each individual aircraft comes from Brussels.
Air traffic control isn’t unified across Europe. The British system is NATS.
However, there’s necessarily a lot of co-operation between ATC systems, and it wouldn’t surprise me if there’s a central collation of such data. But Brussels has no authority over permission to land at Heathrow.