Actually, I sort of agree with mattsccm – I don't think we should just be able to pick and choose which laws we obey.
The law was actually written to prevent carriages driving on the pavement (and so it should have been, 40 people a year are killed by "horseless carriages" on pavements) and was written, IIRC, before the invention of the bicycle.
The law makers, and those charged with upholding the law, have said that riding responsibly on the pavement is not considered an offence, though they have not gone so far as to actually take the offence off the statute books. (Just as laws relating to killing Scots within York city walls after dark with a bow and arrow, or practicing archery on a Sunday, or not eating mince pies on Boxing Day are still on the statute books.)
so only cycle on the pavement wit the child if you would on your own
Okay 😉