naïve - not sure about that.

I didn't mention cracks in your foundations..I mentioned cracks generically...(your mentioning of cracked foundations implies impending structural doomsday(!))

As an architect I know that your Victorian house has very minimal brick footings as foundations and as such any roots wont be effecting them but instead effecting the London clay and local water content of the soil they lay onto. (If indeed your house is suffering active subsidence caused by tree roots). The cracks you see need to be assessed as critical or non-critical to the structural stability of the house, now and going forward.

I guess you haven't had a detailed structural survey undertaking to examine the cracks and their probable cause, solution or seriousness- I would do this first...Victorian properties have lots of cracks..not all of them you need to freak-out over.

also I don't know how easy it is to prove origins of subsidence issues in London soils (possibly clay)? - as there could be counter arguments to the cause.

possibly best to: get a SE to assess actual issue then discuss a solution with interested parties. This would be in contrast to your default - cut it down and launch legal proceedings against Lewisham.

merry christmas