The cleaning process had been “very meticulous”, said Haigh, who has not used any power tools or machinery.
He said “acidic” bird faeces – as well as moss, lichen, pollen and algae – had damaged the memorial.
“We have to take each layer off in stages,” said Haigh.
“The cenotaph has been erected for about 100 years, but the actual Portland stone itself is about 150 million years old.”
He added that he hoped the works would be completed this week, depending on weather conditions.
Councillor Mark Ieronimo, cabinet portfolio holder for transport and infrastructure, said: “The war memorials in Paragon Square are not just historically significant but are a poignant reminder of the sacrifices made by those who served their country.
“By carefully cleaning and restoring both the Paragon Square War Memorial and the Boer War Memorial, we are helping to ensure they continue to be a place of remembrance, reflection and respect for many years to come.”
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