What qld330 said.
The general BA position is here:
httphttp://www.britishairways.com/careers/faq.shtml
Under "Can residents overseas apply..." (sorry can't cut and paste the relevant bit).
Basically as a company policy they don't sponsor except in exceptional circumstances and then they follow UK Home Office guidelines. I suspect unless there's a very strong business case (lack of EU passport holders applying) they won't do it.