Campaigners criticised a pub being in 'bad taste' after the bar, formerly a disused job centre in Deptford, kept its original name.
The property will use mirrors and state-of-the-art glass to give the appearance it doesn't exist.
A woman watched in her bedroom by a man who bugged her webcam tells ITV News of her shock, but backs decision not to jail him immediately.
Police filled up buckets with water and managed to remove the soot that had settled and erase any visible signs of damage.
Detectives are treating the incident as arson and they are combing CCTV. No arrests have been made.
It comes less than a week before the 100th anniversary of the declaration of war against Germany in 1914.
– Superintendent Neil Evans, Lewisham Police
It is very rare a memorial is vandalised and is naturally an emotive subject. This Sunday see's the Eve of the outbreak of WW1 and it is particularly insensitive that someone should vandalise a war memorial which helps us remember the sacrifice that many Men and Women made from around the British Empire.
Lewisham's diverse community reflects those nations that valiantly contributed and therefore the conflict of 1914-18 is a shared community experience. Let us all take a moment to reflect on that and the commemorations.
Vandals have targeted a war memorial just days before Britain marks the centenary of the start of the First World War.
Police were alerted to a fire at the monument in Lewisham, south-east London, early today.
Officers found the charred remains of burned poppy wreaths at the memorial, while there was smoke damage to its base.
Detectives investigating the murder of a 22-year-old man in Downham, Lewisham have charged three men with murder and conspiracy to rob.
Marcus El-Alfy, 18, Lance Slowley, 23, and Jordache Smith-Challis, 19 have all been remanded in custody to appear before Bromley Magistrates Court later today.
A 22 year-old man was found stabbed to death on Coniston Road, Downham on Sunday night after reports of a fight in the street,
The Metropolitan Police said it hopes the guilty verdict handed down to cyberstalker Andrew Meldrum will act as a deterrent and bring "some consolation" to his victims.
– Met Police spokesman
I would like to thank all witnesses in this investigation but especially the three victims who gave evidence on matters that were clearly of a private, intimate and personal nature to them. Meldrum effectively hacked into their lives.
I hope that they can take some consolation in the guilty verdict that sends out a clear message to anyone that this type of intrusion into a person's private life is not acceptable and the Metropolitan Police will support all victims and pursue all suspects.
One of the victims of cyberstalker Andew Meldrum has told ITV News of her shock at learning she was being spied on in her own home but said she supported the decision not to send the voyeur straight to jail.
"Even when I found out about it I couldn't believe that it had actually happened," said the woman, who cannot be identified for legal reasons.
"It was so shocking to see how easy it was and how quickly it was for someone to be able to install it and watch me and to do it inside my own home," she continued.
"It makes you question as a person what you do and how you live your life."
Speaking after Meldrum received a 12-month suspended sentence for his webcam plot, she said justice had been done, saying: "I believe the judge came up with the right conclusion."
She added: "If this is going to rehabilitate him and make other people think before they do things and if it's going to help anyone then that's fine."
Cyber stalker Andrew Meldrum has been described as a "jealous and controlling" man who pursued his plot for his own "personal sexual gratification".
Sentencing, Recorder Mark Heywood QC said: "It's clear from the evidence that many, many, many recordings were made by the computers of the three young women... concerning the most private acts in their own homes."
In one case, Meldrum conned his victim into believing he could help solve her computer problems but instead installed software which allowed him to remotely access her webcam.
He remained undetected for 15 months until the women - who cannot be named for legal reasons - discovered the programme had been installed on their computers.
Meldrum, a former Goldsmiths University student, has been ordered to forfeit his computer and pay a contribution to prosecution costs of £2,100 plus a £100 victim surcharge.