Getting a replacement SIM sorted the problem for me too, although BT haven't got the message yet, they also told me:
a) it was an iPhone issue
b) getting a replacement SIM wouldn't solve the problem.
Thanks for the solution!
SAME ISSUE HERE TOO. I moved from O2 to BT. BT say it is a voicemail left over from O2. The o2 guru says it is a BT problem as the o2 account and phone number has been passed to BT. BT have said they will get back to me. Here's hoping.
It used to happen when I was EE network, drove me nuts. They will need to reset your mail box as thats how EE sorted the problem for me a few time. Good luck trying to explain that to a call centre! I had it once on my BT Mobile but it had vanished in a few days
Always good to search the history on a problem and see that a couple of years on I now have the same problem after moving from 02 to BT.