Winter shelters, financed by the government and run by voluntary bodies such as Crisis, the Salvation Army and Centrepoint, provide beds, food, medical aid and long-term resettlement help and are open until 31 March.
Nearly 500 beds are being made available under the£3 million winter shelter programme, part of the governments successful Rough Sleepers Initiative (RSI), with additional emergency beds brought into use during particularly severe weather.
Over 100 emergency beds have already been made available during the current spell of freezing weather.
'I am determined that no-one should need to sleep rough, whether at this or any other time of the year, and I am encouraged that so many of those sleeping rough in central London have made use of the facilities the Government is providing.
'The cold weather we are experiencing makes life especially difficult for some, and I would urge those who have not already done so to come in from the cold and take advantage of the help available.'
Mr Curry emphasised the government's continuing commitment to helping those who sleep rough come off the streets and into a better life.
'The Rough Sleepers Initiative, which has been running for six years in central London, has helped several thousands into a more settled lifestyle, providing help through outreach work, medical aid for problems such as alcohol and drug misuse, and the provision of permanent accommodation.
The number of people sleeping rough in central London on any night has fallen from over 1,000 in 1990 to less than 290 now.
'The continuation of the RSI in central London and its extension to Bristol and Brighton, and the money being made available to areas outside central London where there is evidence of a problem, will make an enormous difference to those who have, for whatever reason, lost their way in life and given up hope. Our job is to restore that hope.'