I don't know if you'll want For Want of a Nail, then. That's VERY serious AH. It's AH written in the form of a textbook from an ATL in which Britain quashes the American Revolution. It's very interesting (though a little dry), but if you're looking for a light, fun AH novel to read, that's not it.
Since you're British, you may want to check out The Peshawar Lancers by S.M. Stirling. It's an ASB scenario in which a meteor shower impacting the Northern Hemisphere in 1878 destroys civilization as we know it. The British evacuate the home isles and India becomes the new seat of the British empire. I haven't read it myself, but it looks interesting.
Also, by early 20th century, do you mean up through WWII? If you do, you could also read the two great Nazi victory AH novels (as I was told on here when I asked for Nazi victory reading suggestions a couple years ago), Fatherland by Robert Harris and The Man in the High Castle by Philip K. Dick. Or if you want a super ASB WWII, you could read Harry Turtledove's WorldWar quartet. It's about reptilian aliens invading Earth in 1942 and how the different factions work together to repel the invasion. (No, the Germans, Jews, and Soviets don't all become friends all of a sudden. Turtledove does a good job of reflecting how tense the partnerships between factions are.) If you read any Turtledove, you might want to pick WorldWar because it's not Ameri-centric, and you'll still be initiated in the the weird love-hate Turtledove cult that we have here. (It's kind of worth it to understand all the in-jokes.)
Anybody else have some 18th, 19th, and early 20th century suggestions, preferably Brit-centric?