Same thing applied to me - a few calls over the last few weeks. I stayed on the call yesterday to see what they offered. They asked me for a £300 'deposit' which would be returned to me after the 'new account' had been set up, which would save me £600 that year. I was suspicious when she had no details at all of my current tariff. I said I was driving and would need to look up my bank details, she was asking for bank etc etc. I agreed she could call me today, as I wanted to check out the security of this with EE directly. It is funny - but she hasn't rung me back today! Do be careful. I have reported this to EE.
