Many replies about politics and diplomacy, but the OP asked about technology and doctrine.
I think that in the air, you'd have essentially the same level of tech development as in OTL with regard to heavier-than-air vehicles. It's a new field and there is no reason to assume a continued (but very strained) peace doesn't bring about the OTL developments. However, lighter-than-air stuff (dirigibles) are probably still around in numbers. Even with a Hindenburg disaster, without WWI it's not as clear they are too vulnerable to airplanes. They'd be used for maritime patrolling, and possibly expected to be able to carry out night-time strategic bombing.
On the ground, tanks would exist but they would be fairly backward in design when compared to OTL. With no live-fire testing in WWI, there will be several very bad designs around. You'll also have even more mounted cavalry or mixed cavalry units than in OTL. And everyone will be for the attack, not having had the experience of trenches, barbed wire and MGs. Permanent fortifications will be much less fashionable.
At sea, it very much depends if reason and budget constraints have brought about a great powers' naval treaty or not (without WWI, it's possible the fear of constant escalation isn't there). If yes, then the navies and warships might resemble those of OTL, though possibly with less torpedo protection. But if no cap has been placed, you might have battleship behemoths. These will have plenty of torpedo and horizontal protection, given that they will be exceptionally costly.
Presumably, there will have been colonial wars, minor wars, possibly proxy wars. Everyone, not just the British, will be more used to small-scale, lower-intensity operations, possibly counterinsurgency. It is possible that minor wars bring about the knowledge that in OTL was given mostly by WWI, and thus you'd have slightly better tanks, more focus on the defense etc.; but it's also possible that they don't.