I think it depends on your connection/route and ticket. I suspect you likely fail on the "full fare" part of the rules given it's an RTW, and maybe if there are other connection possibilities in between this potentially (not sure of your route).

http://www.flyertalk.com/forum/briti...ded-hotel.html is the thread I was thinking of from a while back, with some very helpful posts from BA employees in there (though do note it may of course now be out of date!). Specifically http://www.flyertalk.com/forum/10942583-post20.html and http://www.flyertalk.com/forum/10942561-post19.html (which also notes this has to be done at booking not after the fact).