Apart from dual carriageways and motorways, British roads are generally going to be a lot narrower and bendier than North American roads. So just stopping, or even pulling over and stopping, may well cause problems rather than solve them.

As a pedestrian I stand well back from the crossing/edge of the pavement, with my arms very firmly around whichever children are walking rather than being pushed, to make it absolutely clear that we're not moving anywhere. We live nearly between the police station and the hospital, and just down the road from the fire station, so sirens are frequent.