Funny, I've been responsible for paying school photographers before now. They charge the school for their services and the school takes a commission on all orders from parents. The profit works two ways.
And yes, schools do manage their own finances, but they still have to justify what they spend and how they spend it. The reason local authorities have this 'approved vendors' system is supposedly to prevent dodgy dealings - like the one that happened here a few years where a headmaster was buying goods from his son's company at vastly inflated prices and then taking a cut off the top. He was also buying other goods and services from other companies on behalf of the school that were really for son's business - VAT free, of course. You'll be pleased to know he was sacked.
We have a list of about half a dozen photographers that schools and other departments can use. If anyone wants to use a different one, then they have to show that the company is the only one that can provide that exact service at the cheapest price. A four-sided, A4 form has to be filled in to provide a business case for it. Depending on the size of the contract, it may have to go to tender, but I doubt this would be the case for a few hundred quid for a school photographer.
It's fair to say that rules are bent. If I have a small amount to pay to a one-off vendor who isn't listed, then I'll write a cheque from our current account rather than send the invoice to finance. It'll still show at audit, but I find auditors tend to be a little more realistic than finance and procurement officers.
It's worth putting your case forward to the school, though, because if your photographer is suitable then the school should be able to use him/her and it could be worth someone filling in a few forms - if they're not too busy, that is!