We use 英国 to mean Britain, and 英格兰 to mean England.
As far as I know, Britain means exactly the same thing as the United Kingdom, which is made up of Great Britain and Northern Ireland, while Great Britain, which we call 大不列颠 in Chinese, only comprises England, Scotland and Wales.
On formal occasions, it is possible to use 大不列颠及北爱尔兰联合王国, for instance, 中华人民共和国与大不列颠及北爱尔兰联合王国关于香港问题的联合声明.