The company I work for require us to phone in on an evening to find out what job we have the next day. Most of the time there is no problem with having delivery times at reasonable times of the morning which can easily be done with start times around 5 or 6.
But we do sometimes get a destination which because of the distance would require a start of 1-30 or 2 am. How does the law stand on this… 
It all sounds ok to me.
Of course, starting at a time before 4am means that days shift counts as a night shift.
This means you can only do 10 hours of work in your shift, unless you have a work place agreement in place.
(Work meaning Driving and Other Work, time on Break or POA isn’t counted as Work)
I would expect the company to cover the cost of all those phone calls and pay an anti-social hours premium for the early start days.