Thank you. The sketch does help but I’m not certain where the gutters are. I assume that they run along the top edge on the plan from left to right although to be honest for the purposes of this answer it immaterial.
I’m also assuming that, looking at the plan, what you want to do is continue the very top left-hand black line in effect all the way along to the right so that the distance between your garage and the top boundary and the other people’s garages and the top boundary is the same all the way along. Please tell me if I am not correct in my thinking.
If the gutters are attached to the Other People’s Garages than those gutters are the responsibility of the people that own the garages. It may be different if there is a gutter between your garage and the other people’s if that is a sort of gully in which case it may be a joint responsibility.
Under the Access to Neighbouring Land Act you are entitled to access onto any neighbouring land for any work required to preserve (maintain) your property hence. If you need to put ladders onto the council land, they have to give consent.
There is no formal process for asking the council to sell you a piece of land. You would write to the Estates Department at the local authority and I would also write to the Legal Department. I would enclose the plan of your property and mark on that exactly what it is that you want to buy. It’s up to you whether you make them an offer or ask them how much they would consider selling it to you for. Unfortunately, if they simply refuse point-blank, there is no mechanism to appeal this that is likely to be successful. There are mechanisms such as judicial review but most unlikely to succeed.
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