As a Spanish, living in Spain and long time driver, I'd say the correct way is the one you describe you do in Britain (and it's the one I do when traffic permits)...
... with one caveat: don't know how it is in other places, but at least in Spain, on any collision, if one driver is switching lanes while the other is not, then the switcher driver is taken as "guilty" and its insurance has to pay the third-party damages (plus for most insurances, you won't get any payment for self-damages): so people just tends to make it on the safe (albeit incorrect) side: if you do the roundabout on the outer lane, you make sure you never switch lanes inside, so no matter if you hit anyone doing the correct thing, or get hit by someone else, you'll get paid for damages.
Yeah, it's absurd, but ask this question to spaniards, and you'll get this answer most of the time (I have).
Fun extra fact
In my specific region (Murcia, on the southeast), whenever there's not a high load of traffic (and sometimes even if there is), if you need to exit on the other side of the roundabout, people will tend to just drive straight (or almost) through roundabouts, so using basically all lanes. And yes, in folklore, we often get cricitised by it (and rightly so).
Additional "Official" fact
This is what the DGT (the transport principal in Spain, or Dirección General de Tráfico) says you should do on roundabouts (source, from 2014: http://revista.dgt.es/es/multimedia/infografia/2014/1008-Como-circular-en-glorietas.shtml ):
Seems they are actually encouraging the usage of the outer lane (in the image, "Bien" means "Good", and "Mal" means "Bad"): The only cars doing it clearly good
are the blue ones (car "A"). There's also car "B" which does it right, but it seems to come out of nowhere (it's already in the middle of the roundabout), and since "D" (which is what I described in the fun fact above) does it wrong by changing lanes, there's no other "correct" endorsed way.
I find all this very wrong (why would they make more than two lanes anyway, if using the inner lane would be always wrong?), but just adding it as it has some "officiality" to it.
There's also one animated video on this link (from May 2016)