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I don’t know what you mean when you say the neighbour has claimed the hundred millimetres of boundary. The boundary is an imaginary single line.
If your garage wall is absolutely right on the boundary, he can build right up to it but not attached to it. For practical purposes therefore, he cannot do what he is proposing.
If however your garage is slightly offset over the boundary towards you, then he can only build up to the boundary which may leave a slight gap.
What you might want to do is tell him that you will agree for him to do this provided he gives you a chunk of money and pay for any legal costs. What he’s trying to do is save the cost of one garage wall and also gain that little bit of extra width.
Can I clarify anything for you?
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