Q: New iPhone 6s not recognising my Apple ID

I'm not sure who EE is (where you bought the phone).  But, I suspect the phone is asking for the PREVIOUS owner's AppleID.  If so, unless you can contact the original owner and get them to remotely unlock the phone, the phone is USELESS to you (or anyone else) and NO ONE can help you - even Apple.  Try to get your money back from EE.  You can also see this link:

Turn off Find My iPhone Activation Lock - Apple Support

Please provide the exact text of the error that you see when you attempt to activate the phone. Exactly what it says makes a big difference as to what the problem is.

This was during the activation process? That makes it sound like Activation Lock, and that would mean the device wasn't new, and had already been activated in the past.