Going to answer my own question after searching the web a bit more...
The setting is not in the Notification Center, where you'd expect... it's in the Calendar app on OS X, and in the Mail, Contacts and Calendar settings in iOS 6 (don't know about 7 yet 😉).
In OS X, open your Calendar and from the menu bar choose Calendar > Preferences and then highlight the Alerts tab. Second from the bottom is a checkbox labelled "Turn off shared calendar messages in Notification Center"... it's unchecked, and you need to put a check mark (aka tick) in that box. To be honest, I think this is poorly designed, because putting a check mark in a box to disable a setting is rather like a double negative, and probably why I've seen so many people think they have this set correctly when in fact the opposite is true.
There's a similar setting on iPhones/iPads too, and again it's hidden away, but at least it's the right way round. Go to Settings > Mail, Contacts, Calendars and scroll right to the bottom. Where it says "Shared Calendar Alerts" change this setting to "OFF" (it's ON by default).