Does management have to grant me a transfer of can they refuse? (UK)

Hello everyone! I'm a shift manager at a McDonald's near my uni, but I will be graduating soon and plan on attending a postgraduate program in my home city. I would like to transfer to a McDonald's closer to home and already plan on asking my Business Manager but I'm wondering if he has the authority to deny my request? I can commute from my house to the store, but it's an hour train journey and then another bus journey on top of that which takes like 2 hours and that's just not feasible in my mind. I have commuted to the store before over Christmas break but I always ended up being late because of unreliable trains so I don't think it would be a good idea to commute long term.

The only problem is that a fair few managers at my store are leaving or demoting themselves and they're currently struggling for managers. I've also seen my boss deny transfers to old managers that no longer work at the store so I'm wondering could he do the same to me? If he does deny my transfer, I'll just hand in my notice and enter the job hunt again but I'd prefer to have some job security at least. So that's why I'm asking if he is allowed to deny my transfer if I find a store willing to take me on. And if he does, are there any steps I can take to report him if that's an option? Thank you!