Hi.
We have noticed the same issues within the Worcestershire BB network.
Are you a school connected to an LA WAN?
If so, here is our theory....
Apple launched a new service just before the launch of iOS7 called Apple Caching Server 2. This gets installed onto any MAC server on a network. This MAC Server then registers with Apple as that networks local caching server. So any requests from an iOS7 device to apple, get re-directed to the registers Apple Cache Server on that network.
In our instance we have some 260 sites connected, each with their own firewall. So if one sites MAC Server registers with Apple (gets logged against your external IP Address) then all other internal iOS7 devices get re-directed to this box. In our case this can't happen as the site in question is on a low bandwith connection and we don't want all devices going there.
We would be better suited to get a Caching Server sat at the core of our network that all devices in our connected sites can talk to.
Its an Apple issue/problem and they don't seem to be very forth coming with a fix.
Hope that helps!