It is not illegal in the UK to shoot and drink. Mind you, if there was an accident and you were considered by the police to be intoxicated, I wouldn't give you much chance in retaining your shotgun certificate or firearms license.
As has been said, on a days driven shooting here it is usual to find an alcoholic accompaniment to elevenses. Bull shot, sloe gin or even a slowgasm (mixture of sloe gin and champagne; try it, its very refreshing) is not unusual. Then at lunch a drink before the meal, with wine during it and even sometimes, a glass of port at the end, with a cigar. Now these are pretty special days for me and not necessarily the norm. On my regular, less smart, shoot someone will pull out a hip flask with sloe gin or the Kings ginger for a quick nip between the second and third drives and there will be sherry or wine at lunch. Maybe port at Christmas.
All this probably reads as if we are soaked in alcohol and waving our 100 year old fine English shotguns around with abandon. But I have shot in the UK, Europe and the Americas with judges, chief constables, justices of the peace, members of parliament, chiefs of defence staff, global business chairmen as well as farmers, estate agents, policemen, builders, wage slaves and all sorts. Never once in 50 years shooting have I seen anyone behave irresponsibly or dangerously with a gun in their allegedly alcoholic hand. That's not to say that accidents have and will continue to happen, but it has not been my experience nor that of others I have shot with.
Please note I am not being judgmental. I am merely recounting personal experience.
Tim