The blaze at the Grade II listed building began last Friday night and 80 firefighters fought for over three hours to extinguish the flames.
No one was injured and the council says it recognises the impact of the fire on the community around Mitcham Common.
The Burn Bullock was named after the famous cricketer associated with the nearby Mitcham Cricket Club.
But it has been derelict for a decade with nearby residents complaining about squatters and fly tipping at the site.
Merton Council has confirmed there have been people living in the site.
The council said it couldn’t speak to us because of pre-election guidelines.
But in a statement the authority says it has; “acted many times with partner agencies to try to ensure the safety of the building and those living in it, including as recently as last year.
“But the council has very limited powers to further intervene because the building and land is privately owned.”