let me take a whack at this.
first off the two hour business...at some destinations, like islands, with no reasonable alternate nearby, 2 hours of extra fuel is carried in llieu of an alternate...I can't imagine anyplace in the UK where this would count.
airports are not closed due to wx...airports are closed if there is an accident and the crash fire rescue people are responding to an accident...the authority of the aiport (manager, not ATC) can have a letter of agreement with ATC to close the airport on their behalf if fire crews are responding and could not respond to an additional accident.
clearing a runway with snow is another reason that the managers can close the airport, but fog or thunderstorms are not reason t o ''close'' an airport.
ATC may limit IFR departures or arrivals to allow planes to maneuver around thunderstorms.
The captain can choose to divert as he chooses. in the USA a dispatcher can also choose to divert his flight with concurrence of the captain...but the final authority is always the captain.
YOU may make as many attempts as you like to land...no regulation against a dozen tries...however, it is considered prudent to try the approach once and if a mistake is made, or weather improvements or other improvements are noted, another attempt can be done. After this, it is considered good form to divert...however it is not a regulation.
Yes, FUEL is king...and rarely do you have enough for more than a couple of attempts before diverting.
AS to the 911 shutdown of USA airspace, that was a unique situation involving national security regulations which have been on the books since the start of the cold war.
Long haul flights have no priority.
Low fuel may be declared using the phrase: MINIMUM FUEL...ATC will then advise the pilot if he cannot be given a guarantee of no delays...if delays can be expected ATC will ask where the pilot wishes to divert to.
One can declare an emergency and be granted priority landing attempts, but that is a whole other can of worms.
I've attempted an approach three times into chicago midway as the wx was reported at approach mins but we never saw the runway...we had lots of fuel and then went to indianapolis and spent the night.
many factors can affect the success of an approach, even sun angle!
so...if anyone tells you different, its questionable...again these are US regulations...and we can only START an approach if the airport is reporting satisfactory visibility conditions.