In the UK we generally do the one-at-a-time thing too and I would be pretty horrified if someone I was dating told me he was seeing someone else/playing the field. I wonder if exclusivity carries a slightly different meaning. What I'm reading is exclusivity infers a serious relationship. It doesn't here, necessarily. It just means that you only date one person at a time. There's no long-term commitment involved, one or other of the parties can still end the relationship if they don't want to take it any further, but you don't date/sleep around. It's seen as very poor form here and most people would consider it two-timing or that the person doing it was a player.
Dating seems to be far more of a direct activity over there. Here, we seem to do the dance a little more, which probably ties in with the ask/hint culture thing we've had so many discussions about (although we do have askers, hinting is much more the norm here). In my experience you probably wouldn't ask someone out in the first place if you weren't at least a bit interested in having some kind of relationship with them. You'd generally meet someone in a social activity, get to know them a little bit, decide that you're interested in them, maybe develop a bit of a crush on them then spend a while working up the courage to 'ask them out' (and the other person probably wouldn't agree if they weren't reciprocally interested). So, by the time you get to 'going out with someone', you already pretty much know that you really like them and the 'dating' phase is more of a 'see if it works out' kind of thing. If you're asked out for a second date it's pretty much understood that the person doing the asking likes you and is interested in progressing things.
From what I'm reading here, dating in America seems to be the complete opposite: ask someone out if you like the look of them, *then* decide if you're interested in them, so, I can see why the 'dating multiple people' thing happens.