I have a referee's whistle next to the phone, with which I sometimes leave a very loud 'message'! I have caller ID, but DD1's number is withheld, so I do have to answer those, but ignore the international and 0845 ones.
I was told that these centres call 10 numbers all at once, and as soon as one is answered, the others are cut off resulting in the silent calls. 
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I no longer get the "silent" calls but now when I answer a recorded voice tells me my call cannot be taken at this time and to leave a message! I started off by politely asking them not to ring again but after the 5th one this week I feel like threatening to track them down and cut out their hearts
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