In Scotland you can shoot game on Sundays but it is generally not done.
You need a game licence in Scotland to shoot game. Game includes hares, pheasants, partridges, grouse, ptarmigan, blackgame, snipe and woodcock. As stated in above posts deer may or may not require a game licence depending on whether the land is unenclosed or enclosed. There are also exceptions for hares.
There are 4 game licences available:-
an annual one costs £6 and expires 31st July
a short one costing £4, which runs from 1st August - 31st October,
a short one costing £4, which runs from 1st November - 31st July
an even shorter one costing £2 which lasts for 14 days.
They all cost more to issue than they bring in in Revenue!
So the Police at Caerlaverock are acting "ultra vires" ie outwith their authority unless the wildfowlers had shot, or were shooting at game as defined by the game laws or it may be specified in the permit conditions for Caerlaverock that you must have one. I have never shot at Caerlaverock so cannot say about the latter point.
A quick call to BASC should sort it out and get the police a slap on the wrist.
In the circumstances I would also put in a complaint to the Chief Constable requesting some training for the officers concerned, an investigation to ensure they were not acting on any prejudices the individual officers may have against field sports, a written apology from the police concerned, the return of the guns in a cleaned and undamaged condition as well as recompense for loss of shooting, accommodation and other ancillary expenses.
You may only get a verbal apology but it will make them think twice before doing it again!
Bob