A shed to me implies it is a decent-sized walk-in, not one of those tiny elevated coops. That helps me to visualize. I know it seems cold to you, but in England you really don’t get that cold as far as chickens go. Still, it gets cold enough for you to be concerned about frostbite.
Any time it gets below freezing frostbite is possible. Just like the wild birds you see outside, chickens can handle the cold as long as they are housed properly. When it gets really cold or a strong cold wind is blowing, wild birds hide in thickets or other places out of the wind but don’t lock themselves in airtight locations. They make sure they gave outstanding, great, fabulous ventilation. That’s what you need to shoot for in a chicken coop, wind protection but plenty of ventilation.
The biggest contributor to frostbite, other than freezing temperatures, is moisture in the air. Moisture comes from their breathing, their poop, water not frozen, outside water getting in the coop, or maybe something else. Good ventilation up high allows this moisture to escape without breezes blowing on them. Since ammonia is lighter than air, openings up high allow ammonia to escape too.
Nowhere have I said anything about the temperature inside the coop being warmer or colder than the outside air. As far as wind protection, that’s irrelevant. Usually it will be warmer in the coop than outside from the birds body heat, the heat from the poop, maybe the thawed water is a little warmer than the air, and with a coop on the ground during cold snaps the ground is usually warmer than the air temperature. In some coops this temperature difference will be noticeable, in some not really noticeable but it doesn’t need to be much. You’ll still get air movement with good ventilation up high. The only time II can envision the inside temperature being cooler than outside is when the outside temperature is increasing fairly rapidly. That’s not going to be a concern.
If you can smell ammonia you probably need to do something. Good ventilation up high will allow it to escape without building up, but it’s still not good for you or your birds to breathe. Ammonia is created when poop composts or breaks down. It’s not noticeable unless the poop is thawed and kind of wet. Wet poop is dangerous to your flock, not just from an ammonia standpoint but also from a disease standpoint, some bad things can live in wet poop. What you need to look at is why the poop is wet.
Wet might come from rain or snow blowing into your coop. If the coop is in a low spot rainwater runoff may be collecting there. If your waterer leaks or the birds spill it, you can have a wet spot. Another common cause is that the poop builds up so thick that it doesn’t dry out. You may need to remove the pop before it builds up that thick.
I don’t know enough about your specific situation to give specific advice, I can only be general. Don’t be shy about providing a lot of ventilation up high. Don’t worry about temperature. Keep the coop dry.
Good luck!