What would be the best firearm for a survival situation

Cant have a handgun but this is allowed

www.gunstar.co.uk/dsr-precision-dsr-1-bolt-action-308-rifles/rifles/937869

As are most shotguns including semi auto .

And live 105mm field howitzers.

Any firearms and ammunition may be kept in the home in a locked case secured to a wall.

You forgot unrifled field guns. They can be held on a shotgun licence

Also to entertain the thought more, make sure you're in peak physical fitness, you're going to have to be relatively strong and have good endurance

OP, based on your listed requirements, I'd probably be looking for a Savage or Ruger Scout rifle in .308. Both have detachable magazines that you would want to stock-up on, but other than that, they offer good performance in an affordable package. I'd prefer that they used M1A/M14 magazines, but only the Mossberg MVP uses those right now and I'm not a fan of their rifles.

.308 Winchester/7.62x51 ammo is plentiful, accurate enough, and powerful enough to satisfy your needs.

I would also highly recommend a .22 rifle and pistol, a good 12 gauge pump, and your choice of a 9mm semi-auto or a .357 magnum revolver stored securely but where you can access them in a time of need. This provides you with a solid firearm foundation that you can then expand upon if you feel the need. Make sure you have a good supply of ammunition and spare parts for your basics prior to adding additional calibers. 

One thing I've seen repeatedly amongst my friends and fellow shooters is a partial preparedness mindset that only focuses on weapons. They love to go on and on about how "ready" they are, and what guns and ammo they have, but when I ask about their food/water/first aid supplies they look chagrined and mutter things like "I'll get around to it". They like to focus on the "tactical" and ignore the practical as it is not "fun". 

I've always liked the idea of having one of the large caliber hunting air guns. Easy to maintain.

Ok, here's the good news; at least you're thinking about it! That puts you ahead of 95% of the population.

Off the top of my head:

A quality rucksack that you have practiced with. Gear is great but you have to be able to carry it.

I cannot stress how important it is to be able to make fire. Think about it. Fire allows you to convert raw meat to food, boil water to drink, provide light and heat in the night, ward off natural predators, and it makes a dandy weapon if needed.

Quality rope and/or paracord. Often overlooked but unbelievably useful.

Water filtration. With all the crap that's in our water supplies, this is a critical element. Dysentery can kill you or, at the very least, make you wish you were dead.

A well stocked first aid kit with a manual. Sewing yourself-up sucks. (Been there) Bleeding out because you didn't know how to stop it sucks harder.

Fishing line and hooks. If there is a nearby steam, odds are there's food swimming in it. Also, good monofilament line had dozens of uses from emergency sutures, snares, sewing-up torn fabric, building shelter, all the way to tripwires and defensive applications.

Flashlight with spare batteries. Should be part of your EDC anyway. Yeah, sooner or later the batteries will die, but this is too useful to ignore.

A map and compass. And learn how to use them. Sure, GPS is great, but not only will your batteries eventually die, there are many places that the signal doesn't reach.

Sounds like my bug out bag minus a few days of food packets.

Absolutely necessary...topo maps don't have batteries that die and don't have to worry about EMP. They're pretty easy to read, are large enough to clearly read the contour lines.