Having spent the first 35 years of my life in that absolute effing void of a place, i can tell you first hand:
Guns? No. It's going to take you 2-4 years to actually buy a centerfire IF you become a citizen. You could get a .22 inside of 8 months IF you're a member of a target club & are prepared to store your rifle AT the club. Hunting permission on farmland? Not a cat in hell's chance. If by some miracle you DO pull that off, the police FAO will need to come & check the land to approve it for rifle hunting. Then come check your house to make sure you have the approved storage safes (1 for ammo, 1 for your firearm. Both bolted to at least 3 solid brick or concrete surfaces) with keyed entry & that nobody in your household has access to your keys but you.) Get a speeding ticket? You lost your guns. Post the wrong thing on social media? Lose your guns.
I cannot adequately describe just HOW anti-firearm the UK is. It honestly makes California, Chicago & NYC look outrageously conservative. Shit, most gun shops won't let you through the door without your firearms license & no, I'm not kidding.
Hunting? Not without extensive training, licensing & a rifle. Also, a red deer stalk in the Highlands is going to cost a fortune. And you don't get the meat. I mean, you can BUY the antlers back, if you want.....
European hunting: Easier than hunting the UK, but insanely prohibitive for non-gun owners.
You get the point.
You can move there, or you can hunt. Pick one.