Actually, there's a similar discussion going on over at
http://www.flyertalk.com/forum/Forum15/HTML/004435.html in which someone has found
this page on the
www.britainusa.com site, which says that "The requirement to hold a visa is normally waived ..."
That gives a big pointer to the direction in which discretion is normally exercised.
Given the number of countries on the "visa national" list whose nationals would benefit from this "transit without visa" concession, I would be surprised if BA did not participate according to its spirit - ie to let pax travel if there is proof of confirmed onward travel within 24 hours and all the other required documents.
[This message has been edited by Globaliser (edited 07-01-2003).]