Why are there no mobile phone masts at Chatsworth?

Been to Chatsworth recently?  Tried to get a mobile signal there?  Anyone would think that the Duke of Devonshire had an aversion to a mobile phone mast being anywhere near the country estate.  I don't know why - there are plenty of the cancer-causing eye-sores designer towers in Sheffield - surely one would fit into the gardens near the other bits of 'modern art'?