though if the walkway is his property all he has to do is put a couple of posts up just next to your garage to support the roof instead, so kicking up a fuss may not result in getting the roof removed totally if that's what you want.
If your garage wall forms the outer edge of your boundary, he cannot attach things to it. What he can do is build up immediately abutting it on his side.
Google 'Party Wall Act' if you want more information on this and the issues that can arise when neighbours want to do this.