Most people find the thought of coping with party wall issues a daunting prospect. The Party Wall Etc Act has many connotations, so it's no surprise that lots of people have difficulties with it.
Things can become a lot more convoluted in major cities like London, which have many period properties and buildings in close proximity to each other. It is essential these issues are handled properly.
Explaining the Party Wall etc Act 1996
The Act provides rights and responsibilities whichever side of the 'wall' you're on. For the party carrying out the task the Act provides for rights not afforded by common law, such as for example access onto the neighbours land to handle some or all of the proposed works, or provide temporary works (e.g. scaffolding) during the course of the works.
You should understand the Act whether it is you or your neighbour who proposes to carry out focus on shared or close by structures. The Act covers focus on structures such as for example shared walls, floors/ceilings of flats, garden walls, and excavations near a neighbouring property.
The overall principle of the Act is that all work which might have an impact upon the structural strength or support function of a celebration wall or might cause harm to the neighbouring side of the wall must be notified.
Some of work included in the Act is listed below:

Demolishing and/or rebuilding a party wall.
Increasing the height or thickness of a PW
Cutting into the PW to take load bearing beams.
Underpinning a PW.
Excavations within 3 metres of a neighbouring building where the excavation will go below underneath of the foundations of the neighbouring building.
Excavations within 6 metres of a neighbouring building where the excavation will go below a line drawn 45� downwards from underneath of the foundations of the neighbouring building.
https://thehearup.com/things-to-consider-before-installing-skylights-in-your-home/34988/ which is not included in the Act includes adding shelves and wall units, replastering and electrical rewiring.
If your planned work on a preexisting structure falls under the Act, you must then issue a notice to all or any affected neighbouring parties. The neighbouring parties must then decide whether they wish to dispute the notice or not.
As with all work affecting neighbours, it is usually better to reach an agreeable agreement. Even where in fact the work requires a notice to be served, it is better to informally discuss the intended work, consider the neighbours comments, and when practical amend your plans accordingly.