Caution - sweeping generalisations ahead!
I think the main difference between US and UK is one of scale. There simply aren't large areas of land or wilderness. Houses are small, gardens (yards) are small. To go and hunt, you need things like permissions, licences, certificates. For example, to have a shotgun licence you must be registered with the local police, who will come and inspect your secure storage. For hunting/shooting, I'd look up BASC (
https://basc.org.uk/ ) to get an idea. I don't shoot (other than the odd pigeon with an air rifle) so can't advise further. There is definitely a class divide in terms of shooting - essentially it is expensive and restricted to those who can afford it.
Weapons are a no-go. Our police are as prejudiced as most others, so while I could probably talk my way out of accidentally carrying a pocket knife to town; my well built Afro-Caribbean friend would get in a lot of trouble. Knives are controlled, a locking knife over 3 inches is classed as a weapon and shouldn't be carried without good cause. So on your land or on the way to your farm is okay.
Prepping is seen as a bit "extreme American" - again I reckon our houses simply can't store that quantity of supplies. No bunkers, unless you've an old Anderson shelter. Some types of people try to keep a stash of food in e.g. a cellar; more usually people who have grown and preserved their own crops.
Home slaughter is illegal for cattle and pigs (iirc?). Sheep can be slaughtered at home but NOT for sale - only for consumption by immediate family. Rabbits and poultry are okay to home slaughter. Bear in mind you will probably have neighbours, and it is not common to see home slaughter - I would be very wary about it depending on whether you are at all overlooked. In terms of livestock, there are webs of legislation around health, the environment, traceability of meat in the food chain, traceability of diseased animals, tracking who has which animals on which parcel of land. I still have to double check things in case they have changed (which they do, frequently). Your own eggs can be sold from your gate or directly from you; but to sell to a third party (e.g. a pub that uses them for cooking) you need to have eggs graded and stamped for traceability. Raw milk is illegal in Scotland, and availability is sporadic in England.
All land is owned in England and trespass laws apply (Scots have a "right to roam"). You can't just find a nice tree in a random wood and chop it down for fuel. You technically can't walk on the land if there isn't a right of way ( e.g. a documented footpath or a permissive path).
I think that's the gist of the cultural differences, so to speak.
In terms of climate, we don't have one. We just have weather. Lots of it. Nothing very extreme, but you can get it all in one day (which is why nobody spends millions on snow ploughs or air con - you just struggle through the 5 days a year you would REALLY REALLY LIKE those things)
Hope that helps a bit?