Help with vocabulary

Ever since Amy outgrew her pram, she's been sitting in something we call Buggy in German.

I wasn't sure what to call it at first, so I went with stroller.

However, it seems that this is a predominantly US word, and I'd like to use a British word instead. I'm not sure what word is used for those things, though -- I got the vague impression that they used to be called pushchairs but that buggy is becoming common as well.

Can you (UK English speakers) help? Is there, perhaps, a difference between the two (e.g. a pushchair is simpler than a buggy); is the difference regional; are both words synonyms and in common use; is pushchair old-fashioned; etc.?

( Here's a poll with a couple of images )