At its peak, the British Empire would control a quarter of both the land and population of Earth. Even then, it wasn't even the strongest industrial power. That was the United States, their former colony. Today, that former colony is now the world's super power.
Had the 13 colonies stayed in the Empire and spread across the continent, could the added resources, population, and industrial might be enough to conquer the world?
A few thoughts on if the colonies remain:
1) They eventually become a commonwealth nation, akin to Canada -- they won't be an organic part of England
2) This probably implies that the British avert the ARW. This gives them more resources in fighting France, probably aiding/speeding that.
3) British / colonial forces will likely seize a few French colonies in America during the Napoleanic Wars, but certainly don't get a Louisiana Purchase. This has two effects: a) Much of that region remains semi-contested, slowing growth. b) Where British / colonial forces gain there, the British will decide what happens with that land -- new colonies, grants to English nobles, etc.
4) The Commonwealth of America (CoA) (AKA US) may spread across much of the continent, but the boundaries between it and Canada are almost certainly different. Alaska will probably be part of Canada, as will parts of what are now Washington (state), N. Idaha, Montana, and the Dakotas.
5) The British might avoid a war with Mexico or conduct it quite differently. So the CoA might not get California, AZ, NM, TX, etc. Instead, the British would be more interested in the coasts and less in empty deserts. So, the borders would again be different -- CoA might extend down the W. coast to Baja, and on the E. might include the Yucatan; however Mexico keeps S. AZ, NM, and TX (possibly as far up as a line from Odessa-San-Antonio-Corpus Christi).
6) The British would be more likely to keep Hawaii as a semi-independent kingdom (since that's what they'd done until the US got involved).
7) The ACW is probably avoided and that did a LOT to spur US industrial growth. Without it, you have less disruption and loss, but less growth and innovation.
8) The "Indian Wars" go differently, with different arrangements at the end.
So, the evolution of what's now the US would change significantly and the British would only gain part of that strength (as a commonwealth).