The 200-year-old building, which is around the corner from the fashionable Borough Market in south London, is being sold by Southwark Council and comes with a reserve of £2.3 million.
The Grade II-listed building needs extensive repairs and refurbishment, but despite this experts said it could fetch far more than its asking price because of soaring demand from private buyers and developers keen to purchase a rare family home in the heart of the capital.
The Labour-controlled authority plans to use the millions raised from the sale to help meet the large costs of building and refurbishing council homes in the area.
Chris Coleman-Smith, head of auctions at Savills, which is carrying out the sale, said: "We think this will be the most expensive council home ever sold, and we're delighted that the proceeds of sale will contribute to creating more housing in the borough."
He added: "It could go for much more than its reserve, it will go up from there in price, it just depends where."
Mr Coleman-Smith said the building had sparked interest from dozens of developers and private buyers from London and abroad.
He said: "We have had all sorts look at it - foreign buyers including a gentleman from China, local people, owner occupiers and developers.
"There is interest in it because it is unique - we don't get many historic buildings coming up like this, but what it goes for remains to be seen.
"London is very popular, whether it is demand from the existing population or buyers from Europe or abroad, it is very, very popular.
"I think the boom will continue for a little while longer."
Built in around 1820, the property is believed to have originally housed managers or directors of the Anchor Brewery before being taken over by the brewer Courage, whose historic advert is still printed on the side of the building.
It was acquired by Southwark Council when the Greater London Council was wound up in 1986 and has stood empty for many years.
Councillors said the cost of repairing the Georgian building meant that auctioning it off and reinvesting the money into new housing stock made the most economic sense.
Councillor Fiona Colley, cabinet member for regeneration, said: "The costs of repair and refurbishment, coupled with the sale price mean that selling this building was always the best option. The receipt will contribute to our new 11,000 council house building programme."
Councillor Ian Wingfield, cabinet member for housing management, said: "Selling council homes is not something I would ordinarily advocate, but this is a no-brainer in terms of the capital we'll receive to invest back into housing, for improving existing stock and new build."
According to the Office for National Statistics, house prices increased by 8.7% in the 12 months until August.
The property is one of the lots to go under the hammer at the Marriott Hotel, Grosvenor Square at 9am.