Can state (academy) schools insist you buy their uniform only from one (on campus) shop?

[BlueberrySkies]

I thought this wasn’t allowed. They want the uniform to be branded (even pe uniform). They are saying everything must be bought from their own specified shop.

It’s going to get (even more) expensive 🙁

They can through some odd loophole many places have found.
It's appalling practice in my opinion and in always wondering who is making the profits here, because it's not the schools.

According to DfE guidance:

The school uniform should be easily available for parents to purchase and schools should seek to select items that can be purchased cheaply, for example in a supermarket or other good value shop. Schools should keep compulsory branded items to a minimum and avoid specifying expensive items of uniform eg expensive outdoor coats. ... Exclusive single supplier contracts should be avoided unless regular tendering competitions are run where more than one supplier can compete for the contract and where best value for parents is secured.

However, that is only guidance, not statutory. I really think schools should be heavily marked down by Ofsted if they operate this sort of practice.

Who owns the specified shop? A relative/ friend of the headteacher?