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“become or cause a nuisance or annoyance to any of the owners or occupiers of the adjoining or neighbouring properties”
The above clause would normally apply to activities taking place at the property, ie running a business, loud music ie drums etc.
It does not necessarily apply to an extension.
You can as you have done so, object to the council.
Also seek advice from a local solicitor who can check the deeds, and look for any other possible restrictions in the area
As for the caravan, May may be classed as a nuisance. Again check deeds but also local council for this, as often in some areas caravans are not allowed to be kept in the front and / or used at home.