I may be wrong, but I thought you also needed planning permission for substantial demolition... you may wish to check with Lewisham whether your next-door developer has permission (or needs permission) for this.

If you live next door to the site, the planning authority should consult directly with you on any adjacent development. They have an obligation to do this, and also to post a public notice (usually A4 laminated sign) in a prominent place (usually tagged to a lamp post next to the site) informing public of application pending a decision.

There is also Health and Safety regulations covering building works, including demolition, called CDM (construction design and management) regulations. If you feel that anything unsafe is going on with the demolition, you can get in touch with the H+S executive who can close a site down if it is unsafe (for workers or public).

If the demolition involves changes to a party wall (wall that you share with the neighbour) or changes to any retaining structure on or near the boundary of your property, the developer will also need to have a 'Party Wall Award' in place under the 'Party Wall etc Act 1996'. Also any new foundations, retaining structures or excavations on or near your boundary will require an award to be in place. The developer has to pay for your party wall surveyor to negotiate this on your behalf if required (or you can agree it yourself if you broadly agree with what they're doing).