It doesn't matter what type of mortgage the person who bought your uncle's property used. Providing she approached them and told them that she wanted to let the property for a certain period of time, and they approved, there is nothing wrong with it. In fact, this is exactly what I did. You will never be able to establish whether or not she has notified the mortgage company, so your only option would be to complain to the Council.
Have you tried just talking to your new neighbours and telling them how bleeding loud they are being?