Hi, Thank you for your question and welcome. My name is XXXXX XXXXX I will assist you. The council are correct, Planning Permission is only Permission to build the structure within the area. Planning Permission does not account for specific interests and at the same time does not grant rights over your property. If the structure sits on your land then they would need an easement or some other right that you would have to grant them. If the structure is being connected to a shared wall this would be covered by the the Party Wall Act and they would have to enter into a party wall agreement with you. I look forward to hearing from you. So no they could not just build it without recognising your right to your land.
Kind regards AJ