Ah, no. That would be a breach of the BBC Charter.
The BBC is, by Royal Charter, only allowed to make programmes for the domestic (licence fee-paying) audience. If those programmes can then be sold overseas (or to repeat stations, or DVD, but the rule predates any inkling that they might ever exist) and the money spent on making more programmes for the domestic audience, then that's OK and a nice bonus.
But making a programme purely or even primarily to make profits from sales (even if that money is then used to make programmes for the UK audience) is out. Banned. Verboten. Breach of Royal Charter leading to continued operation of the BBC being technically speaking illegal (and as we're talking about a Royal Charter, possibly treason
). That sort of thing.
I'm curious how the BBC News World Service works. Is it technically a separate entity?