It used to be the CO President's Club, but that was at South Terminal. I suppose since they moved to North, you can access it there.
Of course you cannot use the BA lounges with Amex Plat (unless of course you use it to pay to upgrade to J or F

)
Worse case, you can use the Chav (er I mean ServisAir) Lounge. It's about £18 on the door. Though to be frank, it's not worth it (they don't even have a recognised brand of vodka - some craap from Lidl).