EE's traditional contracts have no concept of paying off a phone, or of separating elements of your service. You have one single monthly payment covering everything, which you agreed to pay for at least the duration of your minimum-term but ultimately until you explicitly made a change.
Once your minimum-term had expired, you were free to upgrade phone, stay as you were, change to SIM-only or give disconnection notice. You should receive a text message towards the end of your minimum-term explaining your options, but ultimately, any request to change has to come from you.
New plans are on FlexPay, which is split into two separate & distinct contracts
1: A fixed-term finance loan to pay for your phone, this naturally ends once repaid.
2: A minimum-term based airtime plan for your usage.
Each element has its own independent monthly payment.
