I put everything in separate sealed sandwich bags for ease of finding.
For baby:
4-7 nappies (each in a nappy bag so the nappy bag was to hand when dealing with poonamis)
Spare nappy bags for putting destroyed clothes in that needed soaking
Wipes
Spare clothes set and spare babygrow
A couple of Muslins
A blanket (useful for putting baby down in, wrapping up in, additional "clothes" if baby has gone through everything else, acts as sun shade on buggy)
Nappy cream, calpol, teething gel, sun screen
Clips for attaching muslin/blanket to buggy
Spare hat in case of sun
(Feeding stuff if not breastfeeding)
(Raisins/snacks once weaning)
Disposable changing mat (there will be some places where you don't want to put your changing mat down)
For you:
Bottle of water
Straw for when hands are full
Paracetamol, spare contact lenses, hand cream, sanitising wipes, spare top of baby going through sicky phase, snack, keys, something to write on and with, emergency £20, keys on a string (so you can always find them), packet of tissues. (Mobile charging battery unit for phone)
I would suggest you always put the same things in the same pocket so you can find what you're after in your zombied state or direct others to what you need.