just asked and a taxi driver's advice is DON'T
All taxi drivers have to have a CRB check but only when they start then annually they sign off that they haven't committed an offence. There actual record is checked only every 5 years.
A child travelling without a parent should have an escort (this is the practice with school runs)
It is unlikely that you will find a firm who will do this as the cab driver is also at risk.
Best bet is to ask at the school if there are any spare places.