Kezo – Any “form” of taxi business is “Hire and Reward” which you would need a taxi/private hire operator’s licence, plus a drivers taxi/private hire licence from the council. Also taxi companies have to tender for home to school transport contracts and the cheapest price (factoring in fuel and drivers wages) wins the school contract.
There is another way. If your child has an Education Health Care Plan (EHCP) and qualifies for free school transport you are entitled to a Personal Travel Budget (PTB), some councils name it different like personal travel allowance. Here is a link :
https://www.childrenengland.org.uk/personal-travel-budgets#:~:text=A%20Personal%20Travel%20Budget%20(PTB,works%20out%20more%20cost%20effective.
A chap I know, got £8,350.52 pa, paid across eleven monthly payments of around £759.14 per month for taking their child to school. Just don’t mention to the council that the car you will be using is a motability vehicle. The reasoning by the council authority is if you have a motability car you should be using that instead of applying for PTB, but they probably won’t ask anyway.