Illegal to filter??? I didn’t know that… what about motorways? if there is a traffic incident surely a bike can move along slowly until it reatches the front…
No it isnt illegal to filter, it was cleared recently in court that it was not illegal as long as you are following the normal rules of the road. ie not speeding and driving with due car and attention.
So carry on filtering…
As regards pushing a vehicle on the pavement, its all about causing obstructions and using a motorvehicle on public footpaths…pushing a bike violates both… potentially…but as we all know the police apply these kinds of laws not the idiots of the local council etc…and the police use common sense so do it sensibly when needed and no one will mind…
never ride your bike on a pavement slowly or not…will get you in big trouble unless the police authorise you to do so…
how about wheelie-ing whilst on the pavement? 
I had a similar experience near Wembley Stadium on a macth day. I parked in a bike bay in a side road opposite a railway station. Wehen I go back after the match I found they had closed the road and made it pedestrain only. I was told I could only wheel my bike out with engine off.