They are supposed to, but BA don't seem to like doing it. I tried to do this recently and they refused, but the website does state that they will, so you could try taking a print out of the site to the desk with you
Under "Checking in baggage" section
http://www.britishairways.com/en-gb/...&link=main_nav
Baggage will normally be checked to your final destination, provided your journey is on the same ticket. However, if you hold separate tickets for the flights in your journey, we will only through check your baggage to your final destination if the connecting flights are operated by us or by another oneworld airline.