If there is minimal room for a single-storey side extension, it’s wise to work out what internal width of room you could expect once it is built. I presume that you are concerned about the guttering and fascia overhanging across the boundary with your neighbour. You should allow 150mm for guttering and fascia, plus a further 330mm for cavity wall and drylining. This results in an external width of 3.48m being required.
If your house has Permitted Development rights, you can build a single storey side extension subject to it being less than half the width of the house. This means that your house width needs to be at least 6.96m in order to construct a single-storey side extension with an external width of 3.48m, delivering your desired internal room width of 3m. For other limitations on side extensions under Permitted Development rules, see our video.
Note that there are various reasons why a council might have withdrawn Permitted Development rights. Click here for more details.