New South Wales Police Force said the body of a man in his 30s, named in reports as Nepalese chef Brazil Gurung, was also discovered in the flat, which is above a Persian restaurant in a road lined with bars and shops.
According to Australian media, the couple had lived in the flat in King Street for several months and police believe Gurung murdered Ms Blake before killing himself.
In a statement issued through the Foreign Office, her parents Chris and Sharon said: "We are deeply shocked and saddened by the sudden passing of our much loved daughter and sister Amelia, who will be truly missed by all who knew her.
"We would like to thank everyone for the love and support shown to our family.
"As we try to come to terms with losing our beautiful girl, we would very much appreciate privacy at this extremely difficult time."
Emergency services were called to the scene three miles south-west of the city centre at around 5.30pm last Friday after concerns were raised for the welfare of a man and a woman at the property.
"Police attended and discovered the bodies of a woman, aged in her 20s, and a man, aged in his 30s," police said.
Ms Blake, from Loughborough, in Leicestershire, had been travelling around Australia, recently working on a fruit farm in Victoria, and had reportedly been planning to set off travelling Vietnam.
Friends paid tribute on Facebook, with Ellie Mackness saying: "Whenever I saw her she always made me smile or laugh.
"She was the most warm hearted, bubbly, loving and down to earth women I knew."
A former colleague told Australia's Daily Telegraph Gurung had money worries and was "very depressed".
She said the former chef at the Fogo Brazilia Churrasco restaurant, where he met Ms Blake, had feared becoming homeless and described his life as a "living nightmare".
Police said they were investigating the circumstances surrounding the deaths.
A police source told the Press Association the woman is thought to have been the victim of a murder-suicide.
Newtown, the suburb that flanks King Street, is known for having a youthful and diverse population.
The area is popular with backpackers and foreign visitors attracted by its nightlife, cafes and cheaper rents.
A neighbour, who only gave his name as Angelo, said: "I'd guess there were four to six people living in there, I see the owner once every blue moon when he comes to collect rent or whatever.
"I feel sorry for the girl. My first reaction was 'she's 22? A bit young to be on her own'."