My phone number is attached to iMessage so any incoming texts will disappear into the Apple servers and be delivered to my iOS devices. This was great when using an iPhone but now basically means texts are delivered to my iPad.
This was something that hadn't even occurred to me until a friend complained I wasn't reading his messages. A quick hunt online turned up Apple's Deregister iMessage tool which is very easy to use. I had already put my SIM in my new phone by this point and couldn't be bothered to dismantle everything so I used the SMS deregister and it worked immediately.
I think I'm free now?