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Not sure, just anectdotal for now.
For reference, in the UK you get zero priority for sequencing, landing, diversion etc. if you complain of being a bit short of fuel or whatever. Pilot has to declare either a PAN PAN (urgency) if they think they may land with fuel below final reserve, or MAYDAY (distress) if they know that they will. Either of these will usually see the seas parted before them.
The problem when you have the second largest UK airport suddenly close is that you are likely to have multiple instances of PAN PAN or MAYDAY and so they have to be prioritised, along with everyone else who hasn’t declared an emergency yet.
When an airport like Gatwick shuts down it may be that declaring a fuel emergency is a good way to get to the front of the queue and ensure that you are diverted to Luton and not to Prestwick.