Cllr Flo Clucas, executive member for housing, said: "Unfortunately, cases like this are becoming an increasing national problem as landlords evict people from properties because of booming house prices.
"We try to move vulnerable people out of hotel and B&B accommodation as soon as possible and will endeavour to do so in this case. However, as the city's homeless hostels are full, this task is becoming more difficult.
"If people are made offers of housing, as I understand happened in Ms Huxley's case, I urge people to take them."
Plight of UK's 380,000 'hidden homeless'
OTHER Merseyside councils are also seeing rises in the homeless, although not on the scale of Liverpool.
Wirral and Knowsley said the rise amounted to fewer than 20 families in both their areas.