In the UK, as Dudders has said, the minimum calibre is .240, which in effect means the .243.
It is legal for all six species of deer in England although I believe the Scots have different calibre laws where you may hunt roe deer with a .22-250 for example.
It is an ideal starter round and good not only for deer but also foxes.
For someone starting out with a firearm, the police are more likely to grant a certificate for a .243 than a .300 WinMag for example.
It's a popular calibre, relatively cheap to shoot or reload and covers all bases.
It is illegal to use on wild boar however which is .270 as a minimum if memory serves me correctly.
The UK is also quite densely populated and many hunters don't have the wide open places as other hunters around the world are blessed with so a smaller calibre with a quieter report is deemed more politically correct as it is less intrusive.
This is also why you find most UK hunters use a sound moderator which the police put on your licence with out asking. (At least they did with me.)
I would suggest that although the .243 is popular on the continent, I believe our neighbours opt for the 'modern' calibres over and above it.
So I would agree that the most popular calibre in the UK is likely to be the .243. It does the job and has done so for years.
Most hunters who just want a bit of stalking here and there will often be granted one by the police and unless they hunt abroad they will very likely never see the need to go bigger or different.
And even if they do, I wouldn't mind betting they will be keeping hold of their .243.
I would also add that when applying for a Firearms licence in the UK, you have to declare the calibre you wish to own and the quantity of ammunition you can hold and purchase.
You also have to have land to shoot on which the police will vet and deem appropriate for that calibre.
It seems that the authorities prefer you to have a smaller calibre because it's in some way safer than to have a larger one which surely must be more dangerous.......