I suppose this could run as a separate script to gmail (ie not even a plugin), but it would be nice to have integration. But for that I think I'd need to have extra fields available from admin, such as first payment dates (which may differ from sign up dates, for example if I've had to credit their account with extra time). The plugin would use this data to send out the email reminders.
These reminders would link to a page on gmail with a summary of the next payment. Within this page would be hidden fields that are passed to worldpay when the form is submitted. These include price, what they're buying etc.
If users don't renew admin is notified. The system could be taken further in that worldpay have a "callback" feature, where they can talk to a script listening on your server and send back details of purchases as they happen.
Has anything like this already been created? If not I'd like to talk about how much a system might cost.