There could be an insurance implication and a local authority licensing implication.
I don't think they fit the criteria of being School Transport:
(from Reading Borough Council): “School transport vehicle” means a vehicle that is used for the transportation of children/social services clients under a School Transport Service (STS) contract.
They are not under an STS contract, which I presume is something that the council arranges for pupils entitled to free school transport. So I don't think it fits with that license.
I feel they need to be providing some childcare, then they are not a Private Hire or taxi. So could they take the children to your home and stay for a little while?
As a nanny I have insurance that covers the children in my care going in my car as part of my job. Problem for you is that you are not offering a nanny job unless they are providing some childcare... so solve it by having them provide some care.
I agree, it's a snarly one! Local borough council licensing department may be worth contacting for clarification as to what they consider is a Private Hire Vehicle, a Hackney Carriage and a School Transport Vehicle.
Some legislation is www.legislation.gov.uk/ukpga/1976/57 though it may not be that helpful.
This document is worth a read: www.gov.uk/government/uploads/system/uploads/attachment_data/file/3985/phv-licensing-guidance.pdf
Private Hire Vehicle is defined as:
“A motor vehicle constructed or adapted to seat fewer than nine passengers,
other than a hackney carriage or public service vehicle or a London cab or
tramcar, which is provided for hire with the services of a driver for the purpose of carrying passengers”
" The Department would discourage licensing authorities from adopting blanket policies on particular types of services, for example a policy which requires all childminders who drive a child to school to be licensed, as often consideration of the specific facts of how a particular vehicle is used will be necessary to reach a decision."
Having skimmed that document, I would say that if they are only doing the school run, then it could require a PHV license. It doing the school run is part of providing childcare, then it is far less likely to need a license.
So get them to provide some childcare, even if you are at home yourself.
The job also needs to be attractive to someone, would anyone really only do just the school run, surely that is not viable for most people. They would be wanting to do say an hour of care which includes the school run... some will want to do quite a lot more time to make it viable for them as a job.