Can't access webmail either and I can also see why. Your paid to work not dick around sending silly emails.
Indeed but that's not the main reason why webmail accounts are blocked. Think about it, the school (and it will most likely be part of the local council's network who actually set the rules), spend a lot of money keeping the network safe. They place controls to stop people bring dodgy files in which takes time, money and effort. Then someone with a webmail account logs on and downloads a funny picture someone sent them via their webmail encrypted link (so the perimeter controls can't even see it never mind do anything about it). Bingo, that funny picture has a virus embedded in it and it runs riot across the internal network.
Now the IT staff have to work out how to get rid of it across the entire internal network. It will take them days, or even weeks to get it all back under control again. Lots of malware means a visit to each individual PC followed by some seriously skilled work to remove it. Some malware just isn't worth the effort so it's a rebuild of the PC.
Or, they could just block webmail accounts. That makes a lot more sense, yes?