Ms Singh, then 25, injected her boyfriend, 26-year-old Joe Cinque with a lethal dose of heroin.

Today, the flat at 79 Antill Street is vacant and has been for some time. Last week, fencing was put up in preparation for demolition.

ACT Housing purchased the unit for $710,000 in May 2016. A development application to knock down the flat and make way for public housing was lodged later that year.

The residence was among four properties, 79-85 Antill Street, marked for demolition.

The proposal was approved in February this year and a builder contracted in April.

Singh was acquitted of murder in 1999 on the basis of diminished responsibility. Instead, she was charged with manslaughter and served four years of a 10-year sentence.

The high-profile case garnered Australian-wide attention, largely due to Helen Garner’s best-selling book, Joe Cinque’s Consolation, and more recently in the film adaption of the same name.

The duplexes are located opposite the Dickson Town Centre at the intersection with Cowper Street.

The four properties, including number 79, will be replaced with 16 one-, two- and three-bedroom units and a basement carpark with the four blocks to be consolidated into two blocks with eight units on each.

Demolition will start next week with construction starting later this month.

The last remaining tenant was relocated to "more appropriate accommodation" last month, an ACT Housing spokeswoman said.

"Housing ACT was required to relocate the tenant of 83 Antill Street Downer prior to any demolition or construction works commencing," the spokeswoman said.

During the consultation period, issues of overlooking neighbouring properties, visitor car parking, and solar access to some places were raised. The notice of approval said the conditions had been met to address the issues.

Construction is expected to be completed in May 2019 with the first tenants expected to move in a short time later.