Welcome to the forums and for your first post - sorry to understand that you're having some issues with your message waiting tone.
Some areas will always have a stuttered dial tone when a feature is active on the line. Dial 1765 from your Virgin Media home phone and we’ll tell you which colour area you’re in. if you are in Blue zone, you will always have the stuttered dial tone.
For any other zone, when you dial 1571, are you listening to the end of the message and making sure you press * to exit?