If the device had been on your contract for at least 6 months, even if that contract has now been cancelled, you can just apply using the Unlocking your device form as the Pay Monthly option and giving the mobile number that it originally came with. For an iPhone it might tell you it's already unlocked.
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To phone EE: The local rate landline number +44 207 362 0200 or Freephone +44 800 079 8586 - Option 1 for Mobiles; Option 2 for 4G WiFi; Option 3 for Home Broadband & EE TV.
ISPs: 1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 20 Meg WBC => 2014: EE 20 Meg WBC