"Does anyone know if or how British aikido differs from other styles of aikido?"
There isn't really a style of British aikido as there is so much variety on our little island (25+associations). Saying that Aikikai style here has been massively influenced by Chiba Sensei, renown for his uncompromising approach, weapons work and powerful technique. We tend to drink more than most other aiki countries I've visited
In my experience if you've trained in one of the man branches (e.g. Yoshinkan, Iwama, Ki, Shodokan)you wont find most other clubs around the world too different as long as YOU are prepared to adapt to their way of doing things. On a personal note, this is how I've also had to train due to lifestyle over the last few years and I don't recommend it as a way of improving your aikido (with a few specific exceptions).