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You mean 'priority'--the concept of 'right of way' in the UK means something different.
It's an interesting question. The expectation would be that the two movements should not be in difficult conflict (the right turn (red) is only permitted for local buses, so low frequency, although I expect a fair few bike riders probably turn right there). As it's a signalised junction, 'priority' is expected to be regulated largely by the signal phases. The left turn (yellow) is on a separate signal phase to the adjacent straight-ahead lane, and in the same phase as the right turn, so that right-turners (red) don't have to wait for straight-ahead traffic to clear.
So, exercise common sense and there should not be any serious conflict. Have you had a bad experience with a bus turning across you?
Bit of an old pic from google street view but does anyone know this turning? After Westminster bridge heading towards Trafalgar Square.
Who technically has right of way (red line or yellow) Or neither?