Well, you're right about it being formal sounding because almost no one uses anything but the common name, 英國. And even in your example, the Eng part of England is still in there and not in the English. So that's my point--in English, the trend has been to use UK, a neutral term that does not contain anything about England or Britain, which there are groups of people that feel very strongly against. But in Chinese, there is this linguistic lag (maybe forever), and England is still a part of the common name for the UK.

In Taiwan, there's a (I find) humorous translation of 蔣中正 as Chiang Kai-shek. It's as if they knew they'd be laughed at if they tried to translate the Generalissimo's name as Fair and Upright Jiang.

Also the competing translations of Tibet as 西藏 (a Qing term that locates Tibet as the West, or in other words, in relation to its location relative to China) and the newer term 圖博, which is much closer to Tibetan (and the English).

Anyways, not even really disagreeing with your original point to call Peking Beijing, but linguistic lag is actually a quite common phenomenon, and while you notice it in this case, there are many cases where things aren't really consistent, but you may not have noticed.

I see what you mean about the lag. I hadn't realized that the trend was to not use the terms England or Britain.

The names of Chiang Kai-Shek is a complicated issue. He went by at least half a dozen different names over his life. One of them was 蔣介石, which he started using in Japan, I think. "Chiang Kai-Shek" is the Cantonese romanization of that. 蔣中正 was a name he adopted when he got closer to Sun Yat Sen (also a non-mandarin romanization from a different name), who was going by 孫中山.