Every teacher is a pseudo-parent
You carry this burden of care whenever you are in charge of pupils, in school or off-site. It is important, therefore, that you always discharge your duty in compliance with the school's policies and procedures. If you do decide to go your own way, you will have "gone on a frolic of your own" and might well be held responsible for anything that goes wrong.
The school's duty of care stops at the school gate, apart from organised off-site activities. It is not normally responsible for the safety or discipline of pupils on the way to and from school, and especially not on school buses. But some schools feel a need, often for public relations purposes, to take on this jurisdiction. If they do, they must discharge the duty. This can be difficult, since staff are not obliged to participate unless contracted to do so.
Nor are schools responsible for the safety of pupils outside the advertised start and end of the school day, unless they decide to be. The pupils belong to the parents, who resume responsibility once the school's duty has ended.
On the other hand, school staff never actually escape their residual pseudo-parent status. Where it is reasonably practical to do so, a teacher has to safeguard a pupil's safety, even off-site or out of hours. Thus you would be expected to lean over a school gate to warn Darren not to run across the road, but you could not be expected to have a loud-hailer handy to stop him doing the same thing 200 metres away.
Chris Lowe, Former headteacher, trade union legal consultant and chief editor of QGP Ltd.