A small point to correct here - you allude to your contract ending yet still going. I presume therefore that your reference to "contract ended" means you have finished your minimum term rather than your actually having given and served 30days disconnection notice. An important distinction.
If you have requested a change to a SIM-only plan, then how long it takes to start depends how you requested it. Doing so over the phone with CS will normally result in that plan being active before you even terminate the call. If you requested it via your myEE online account or app, it my take a couple of days to swap over - but you should receive a text message confirmation.
