Alternate Histories (Hypothetical Historical Scenarios): What if the British Empire never fell?
Answers
I like Thad's answer, saying Britain would basically become a world police. But I think one of the big reasons the empire fell in the first place was the cost of policing an empire with so many geographical borders. Being an island state protected Britian, giving a defence advantage that allowed her to put military costs into the navy and combat pirates, which effectively led to the empire in the first place.
But once that empire was established you have to put money into:
1) preventing up risings - who could make a policy that works in such a different range of countries and cultures?
2) defending a huge and complicated border covering a wide range of terrains, all needing different equipment and skills and every part of the border having different enemies.
3) maintaining supply lines to every part of the empire to prevent loosing territory due to a blockade.
4) maintaining trade routes so that it could fund all the above
So to survive the empire would have three options:
1) expand to create more logical and defensible borders, with defensible supply lines
2) prioritise territory IE. Cut off any area that was too hard to defend or wasn't particularly profitable
3) compartmentalise - ensure that segments of territory become self sufficient so that supply lines don't matter and if one is attacked the others help defend. But then that basically results in the dissolution of the empire.
4) create some kind of technological or economic advantage that would prevent any country from wanting to attack or territory from wanting to leave. So for example being the first to develop nuclear weapons and maintaining that advantage, or using economic sanctions to ensure that no country on its border would risk attacking, and no indigenous population would benefit from breaking away.
5) great marketing - make it an empire that people want to join rather than to control. So develop the arts, Internet, and focus on PR and marketing the country. No country has even managed to really control the media through control and propaganda, but given the prominence of America culture, could Britain have developed something similar so that people wanted to join? Even if it could would that result in countries joining who couldn't contribute economically and became a drain? (Hence why the USA and EU turn down applications to join)
So really even if the empire hadn't fallen when it did, it would need a substantial change in direction to make it operate effectively in the long term. There would need to be something "new" that isn't around now to make it happen