I have that with BT every time I call them. Works best on business lines that just have 1 socket on the wall.
Had a fault with BT years ago, basically after much fault finding it was discovered the line was swapped accidentally so customer A got customer B's calls and vice versa. BT wouldn't swap them back 'because we can't just turn peoples phones off and swap them over with no notice'. The irony was lost on the BT operative.