I imagine HR will say it's the discretion of youre manager. I suggest you formally submit you're flexi working application with you're desired hours, there's usually a space to describe how it won't affect the service etc. Then if/when you're manager rejects it you can appeal through HR. That's the advice HR gave me. It does sound odd those hours, maybe they feel they can fill the hours easier with another part time staff member at 0.5. Either way they can't say no for the sake of it they have to provide rationale which HR will chase.
I’d imagine your manager is considering job sharing your post 0.5 + 0.5 WTE, or using that money elsewhere for another post. I asked to go back 0.6/0.8 and my manager said it doesn’t work for the needs of the service and offered me compressed hours instead. I ended up having to find another job because I didn’t want full time or compressed hours. From what I understand any requests can be denied if they don’t work with the service need.
Afraid I have no idea if that’s something she can enforce, worth checking out with HR. Seems odd that part time is fine, but only if it’s 0.5. I guess if that’s what it had to be you could do bank hours to make up the rest if that’d be an option? When I went back to work I did 3 days a week and later decided to start doing a couple of bank days a month.