An arson investigation was launched after fire caused significant damage to Medina House.
Five fire engines were called to the fire - the second in less than two years - at 5.40pm on Saturday (December 20). The swift response to the late-afternoon emergency meant the fire was extinguished before the building was destroyed.
Campaigners have since launched a petition calling on Brighton and Hove City Council to issue a compulsory purchase order to safeguard the Victorian landmark.
Medina House was built in 1894 as a women's Turkish bath; a neighbouring building that used to house a swimming pool has been demolished.
Land Registry records, however, show it changed hands for £150,000 as recently as 2012, when it was bought by Ardeshir Taghan, 59, and Mohammed Jafari, a 58-year-old Iranian businessman.
A planning application was submitted on November 19 by Sirus Taghan, of Globe Homes, to demolish the bullding and build a three- and four-stroey block of eight two-bedroom flats.