The number of deaths last month has increased by more than 5,000, following the second-coldest March on record.
Official figures for the first 3 weeks of March 2013 showed that there were 4,206 more deaths than the average for the past 5 years.
With another 1,000 expected during the last week of the month, this pushes the number of extra deaths to over 5,000.
Michelle Mitchell, Age UK's Charity Director-General, said: 'It’s really worrying that the number of deaths in March this year are significantly higher than the average for the previous five years.
'Cold homes are particularly dangerous to the health of older people and are a major contributing factor to the high numbers of excess winter deaths in this country.
In total, there were 33,500 deaths over the first 3 weeks of March 2013, compared with an average of 29,294 over the last 5 years.
Cold weather payments
The deaths come in spite of 635,000 cold weather payments during March - a result of 7 days of below-freezing temperatures - whereas last March, there were none.
Inevitably, older people are hit hardest by the freezing conditions - on average 90% of winter deaths affect people over 60.
'People living in the coldest homes are three times as likely to die from a cold-related illness compared to those in warmer homes,' said Michelle Mitchell.
'We are trailing behind our European counterparts when it comes to providing decent housing that people can afford to heat, and it is the oldest and most vulnerable who are suffering.'
During the winter of 2011-12, more than 24,000 older people died needlessly, as a result of cold-related illnesses.
Age UK's research shows that 36% of people aged 60 or over in Great Britain stay or live in just one heated room of their home to save money.
Michelle Mitchell said: 'The government must invest new carbon taxes in a programme of energy efficiency to bring Britain’s housing stock into the 21st century and enable people to benefit from the heat they use.'