I think "centuries", plural, is too long for anything much to last since the industrial era. I'm not comfortable guessing past 2032 even without any questions about AI.
The United Kingdom of England and Scotland didn't exist until 1707, and even that was sans-Ireland until 1800.
And yet, even with the biggest empire the world had ever known, WW1 could only be won with the support of another huge empire (France) and the subsequent arrival of the USA; shortly after this, most of Ireland became semi-independent.
WW2 was "won", again with huge support, but a pyrrhic victory from the UK's point of view, and India soon after became independent. The Suez Crisis was 1956, and showed that the old empires of the UK (and France, Union française) were no longer economically hegemonic — even when working together — and the US had replaced them in this role.
Looking into the future, there's no way to guess. The more tech advances, the easier it becomes for a single person to cause enormous, world-altering impacts: hackers are already relevant on the geopolitical stage; there's good reason to think that quality of life is directly related to how much energy a person can process, but once you have sufficient energy per-capita, it's not hard to use a cyclotron to brute-force the purification of weapons grade uranium, or to transmute depleted uranium into plutonium; simple genetic manipulation has been a standard technique for first year biology students for at least two decades, and can be done in a home lab, and at some point we will have risks from someone trying to use this for evil rather than decorative bioluminescence. All these things can topple a hegemon that spends its tomorrows looking at yesterday's battlefield.