Nice routing.
For the Concorde Room at LHR, yes. You’re arriving same day in BA First, so you should have access on arrival. Concorde Room access is tied to flying BA First that day, not whether your onward ticket is separate.
First Wing is where it gets tricky. Since your Athens flight is on a separate ticket in business, technically First Wing access is based on your departing cabin that day. If you’re flying Club Europe on that separate booking, they could direct you to normal Club check in instead. That said, some agents may be flexible if you explain you just arrived in First.
For You First hotline, it’s generally tied to an active BA First booking. Since your return is business on the same ticket that includes the outbound First sector, you should still be able to use You First while that ticket is active. Once all First sectors are flown, access usually drops off.
Separate tickets definitely complicate the ground experience a bit, but lounge wise you should be in good shape.
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