"Britain's" shows possession, meaning "of or belonging to Britain," as in "Britain's laws." It can also contract "Britain is" or "Britain has", as in "Britain's ready" or "Britain's seen growth".
We will reflect the country we aspire to govern, and the sound of modern Britain's is a complex harmony, not a male voice choir. David Cameron
I did not want to put myself on the line, as an Australian playing Britain's greatest comic actor. The fans of Sellers are obsessive, possessive - and aggressive. I did not want to risk their anger - or my own reputation. Geoffrey Rush
Britain's most useful role is somewhere between bee and dinosaur. Harold Macmillan
The position of the United Kingdom is as usual so nuanced that it's difficult to see where they are on the spectrum, but look, that's what Britain's like and we all love being British. Fabian Picardo
Our principles: freedom, independence, responsibility, choice-these and the democracy built upon them are Britain's special legacy to the world. Margaret Thatcher
The next few years are going to be horrendous in the UK. The last thing we need is a Somali pirate-style raid on the few wealth creators who still dare to navigate Britain's gale-force waters. Andrew Lloyd Webber