Coracle...
As a TMA ATCO, if a pilot told me he/she was getting short of fuel my response would be "XXX are you declaring an emergency?".
If the answer was no, I would advise him/her what the holding situation was, and give them the full picture regarding what delay they could expect. This advice may be along the lines of "XXX delay is 15 to 20 mins, hold at XXX on reaching".
The pilot is a very well paid, highly skilled person. It is their decision to call an emergency or not. Being told early that they may be running short on fuel is what I would consider good manners and gives me a warning that the A/C may have to divert at some point. Yes, I will afford the A/C more attention; but other than that, no priority.
It is laid down in black and white what the procedures are and the correct ATC responses. Being told that "we are getting short on fuel" means nothing to an ATCO.... do you know what a pilot means by short on fuel?? It is an ambiguous statement considering it could mean short with regards to company gudelines or any other number of reasons. It's as unambiguous as "climb FLXXX, with a good rate through FLXXX"
If (and this is taking it to extremes but doing so for an example) a company policy was to land with 10T of fuel, why should that A/C be afforded any more priority (and thereby penalising others) than any other A/C in the stack if it does not call an emergency and is merely trying to stay within company (and not safety) guidelines??
If you need to land with priority, you call an emergency. Be it for safety reasons or to remain within company guidelines. You then fill in the paperwork and the reason becomes public domain. This way, other people will maybe learn something or have a memory jogged, thus preventing a nasty incident sometime in the future.
That is why the UK, unlike so many other countries has such a good, open reporting system and is one of the safest places to fly. Pilots and ATCOS are encouraged to report, it educates others.