First and foremost I would find someone willing to confirm for you that the blockage was at the ground level. If this is the case, them I am assuming that the ground floor flat suffered from flooding from the first floor flat, assuming that the waste pipe is communal.

Once you can be sure of that, then I would direct a claim, and possibly inform your household insurers in the direction of Lewisham Homes. From that point im sure the claim will be passed to the relevant authority, and also to the councils claims assessors.

Also do you have in writing from both authorities their confirmation of agreement to the works being carried out.