In order for your neighbour to be able to screw into your fence, house, or garage, they will need to get your permission to do so before they begin the process of installing a gate.
It is acceptable for a neighbour to screw fasteners into a wall as long as the wall in question is what is known as a "party wall," which indicates that it is owned jointly by both parties involved in the dispute.
If the neighbour carries out these actions without first having obtained the necessary authority, they will be in violation of the law, and as a result, they may be liable to face legal action as a consequence of your actions.
If a gate that leads to your neighbour’s garden was hung on your property by your neighbour so that they could gain access to their garden, then you have the absolute right to request that the gate be removed from your property. This is because your neighbour hung the gate on your property in order for them to gain access to their garden.
If this was done by one of your neighbours, then you have every right to request that it be removed, as it is trespassing on your property and should not be allowed to remain there.
If you discover that your neighbour has drilled holes into the fencing around your home, or the wall of your garage in order to install a gate, then it is reasonable for you to conclude that this person has violated the law.
Because these activities are mandated by the law, they are under the legal obligation to remove this and complete any and all necessary property repairs. As a contingency plan, you have the following choices available to you in the event that they are hesitant to take down the gate:
Contact a surveyor and then start the process of working through the necessary steps to receive compensation for any damage.
It is also advisable to attempt to speak to your neighbour, having a conversation with them about the reasons why it needs to be removed and sharing your reasoning with them. A result may be found where both parties are happy and no legal proceedings are needed.