Your neighbour can build as close to the boundary as the local authority
permits except none of their construction can extend onto or over the
boundary on your side
I am mystified that you say that the proposed extension roof will finish
"under" your eaves. Do your eaves and gutter extend over the boundary? If
not then nor can theirs. If you belive yours do you may not have the correct
boundary line.
The same goes for the foundations. They should in theory be approximately
150mm (6") wider than the wall. So in theory without eaves/gutter etc you
should not be able to have a wall closer than 150mm to the boundary unless
building control and planners agree. If eaves and gutter is brought in to
the equation then it would be further back than that