I really don't like those coops you can buy online. They are usually more pretty than practical, they invariably claim to be able to handle more chickens than they realistically can, and they are expensive. I understand that “pretty” is important for a lot of people, especially in an urban/suburban setting, so you can't just cobble something together the way I do out in the country. If you are not comfortable building it yourself, you are likely to get a more satisfactory product by selecting a design and get a handyman to build it for you than buying something prebuilt. There are several designs in the coop section at the top of this page.
There are no magic numbers with chickens, for space required or anything else. What you get a lot are guidelines, suggestions that work for a lot of people in a lot of different circumstances. They are overkill for many of us, but they do keep a lot of people out of trouble. If you have no experience, you have to have a starting place and those guidelines are a pretty good place to start.
I am an advocate of providing as much space as you reasonably can. I find the more space I give them the less hard I have to work and the more options I have to deal with issues. When you are dealing with living animals, there will be issues, whether you are dealing with chickens, dogs, cats, or anything else.
In spite of everything I've said, that coop should work for you, but there are some qualifications. You have to have a run that is predator-proof so they have access to it whenever they want. It really does not matter if the space you provide them is in the coop or the run or even free range, but they need a certain amount of space or special handling. Commercial operations have proven you can get by with less than 2 square feet of space per chicken with no run, but they have to take steps to prevent cannibalism. That's part of why I say there are no magic numbers. Many different things can work, but a lot depends on how you manage them.
Another qualification for that coop to work is that you need to provide more ventilation than that one now offers. Since that is a UK coop, I assume you are in the UK. Unless you are pretty far up north, your winters are not all that rough for chickens. But you will occasionally get some freezing spells. The danger to chickens in cold is frostbite, not them freezing to death with their nice permanent down jacket. Excess moisture in the coop leads to frostbite. You also need to extract the ammonia that develops in their poop since that can lead to respiratory problems. Ammonia is quite a bit lighter than air, so you need ventilation over their heads when they are sleeping. Their breathing and their poop will put a lot of moisture in the air. Warm air holds more moisture than cooler air and warm air also rises. Again, the need for ventilation above their heads. You don’t want a cold breeze hitting them directly when they are sleeping, but openings higher than their heads allows an exchange of air without a breeze hitting them directly.
One nest is probably all you need with four hens, but I prefer to provide a second one. They will probably all lay in the one nest, but a second nest gives you an option if you have a broody hen or a nest hog. You really can get by with just one nest but I just like the extra flexibility. Call it personal preference, not a requirement.
I don’t know if any of this helps you or not. Good luck!
sorry i just had to mention it although it wasn't laid in the nest box but i'm sure they will learn
