Originally Posted by number_6

Spa is exclusively for BA pax, you cannot use it when flying CX (or even QF, as JFK is not a JSA station). CX pays extra for pre-flight dining for F pax, but not for anyone else; don't get too excited, this dining is very basic, cafetaria quality food (edible but not like HKG).

The Concorde room has always been exclusive to BA and not shared with OW. Originally built for the supersonic service, and was very nice (with max of 98 pax per day); now it is a much busier and less nice lounge. Somewhat better food but nothing like it used to be (when the Concorde was still flying). So you aren't missing out on too much by not having access. Of course this means that BA doesn't treat their F lounge as an F lounge, hence the dismal conditions there. The recently opened AA FL at JFK is better than the BA F lounge -- rather unthinkable, but that is how the mighty have fallen.