Rule 62) is pretty clear about segregated cycle/pedestrian paths.
It says "you MUST keep to the side intended for cyclists as the pedestrian side remains a pavement or footpath", the MUST meaning that it's against the law if you ignore their sage advice.
Cycle on the pedestrian side and you could, in extremis, be found guilty of 'careless or inconsiderate cycling', and fined up to £1000.
So all you have to do is obey the blue sign. Such as this one (right), by Clifton Moor here in York. It clearly tells you to stick to the left-hand side.
Except the painted markings tell you the opposite. So, whatever you decide, you've committed an offence.
Follow the path round, off the north end of Water Lane through a housing development, and the painted signs do the neat trick of swopping sides at each end..
And what about pedestrians? They don't know where they stand. Literally. Though they'll probably stand in the middle, with their back to me, listening to their iPod. That's what they usually do.