Posted: 24/03/2015 at 10:34
As far as I can tell, there's a big gap in legislation for neighbouring terrace gardens - I'm allowed to (but haven't) make their garden unstable by digging right up to it, without even telling them, so long as it doesn't break the party wall rules for building's foundations.
I don't think it's a matter of legislation so much as that they could sue you for making their garden unstable and it would be up to a court to decide whether your actions were unreasonable/dangerous.
But, as soon as I build a retaining wall to get the job done correctly, then I will need to inform them, and they can object
If you do any work that affects their property (for instance by interrupting the drainage) they have every right to object. Your idea of 'correctly' might not be the best one!