When is it legal to shoot jackdaws?

A lot of Jackdaws were shot recently in Blagdon, North Somerset and we're not sure if this incident is legal under this year's GL 34, 35, 36 so we are wondering what if anything we can do.

Here are the details of this shooting:

On Friday, 11 December 2020 between 9 to 9:30 am a man on a red quad bike entered a field and set up a hide. Using a shotgun, he shot 3 jackdaws that happened to be in the field. He then took one of the dead jackdaws and stuck it on some kind of instrument with its wings stretched out and placed the whole thing on the ground and retreated behind the hide. The instrument intermittently flapped the dead jackdaw's wings which made it look as if it was landing on the field. This seems to have caught the attention of passing jackdaws as they began landing on the field and each time they did, the man shot them. He shot jackdaws continuously for 3 hours. There is a pheasant shoot nearby but they've been shooting the pheasants since October & there are very few pheasants left. The field where the shooting took place is pasture but one corner was planted earlier in the year with maize (for the pheasants) but the maize is now dead & we've never seen jackdaws in the maize (only pigeons). In fact, there aren't even pheasants any longer in the maize or in the surrounding fields which are all pasture.

The jackdaws were for the last couple of months, up until Friday, 11 December, using the hedgerow trees and free standing trees around that field every afternoon around 3:30 pm as an assembly point for all the arriving groups before the whole lot (numbering in the hundreds) flew to their roost in the trees beside Blagdon Lake (an SSSI). Some of the arriving jackdaws would walk about in the pasture part of the field but  not in the maize. In the mornings we watched the jackdaws rise in a mass ascension from their roost and there were hundreds of them. But, now it is very clear that two thirds of the roost are missing. That is a lot of jackdaws and the ascension by the remaining jackdaws seems more disorganised. 

We read GL 34, 35 and 36 and can't see how this shooting of the jackdaws, given that it occurred in December after most of the pheasants had already been shot, could be legal. Also, the trees used by the jackdaws for assembling and roosting are in a rural area so it is unlikely they were a public nuisance and the fields are pasture except for the bit that was planted with pheasant maize. Finally, we couldn't see that any effort had been made to keep any birds, other than pheasants, out of the maize. But we do realise that the law doesn't always mean what laypeople think it means. I've attached 2 screenshots of the area involved; the pin in the first one shows where the shooting occurred & the second one shows that the whole area is within the Mendip AONB, Blagdon Lake (where the birds roosted)  is both an SSSI & an SAC and the woods around The Coombe are also an SAC. Was this shooting legal or is it something we have to put up with?