At what point do the provisions of the ANO come into effect? I'd guess it's the point when the aircraft starts to taxi under its own power.
So I'm thinking that if the CC want to remove a passenger before the aircraft leaves the gate (and certainly if they want to remove them from the transfer bus), they'd have to rely on the provisions of Section 12 of the Licensing Act 1872 (the offence of being drunk in a public place), rather than the provisions of the ANO.
That said, everything I've read so far about this incident suggests this should have been dealt with before they made it through the departure gate.