A cold weather warning has been issued for Sunday evening and early next week by the UK Health Security Agency.
The Met Office and the agency say a cold snap will hit England between 6pm on Sunday and 6pm on Tuesday.
Temperatures could fall to minus 3C in rural areas and frost is expected.
All regions of England will be affected, but forecasters expect the West Midlands and the Welsh Borders to be the coldest.
Temperatures will plunge at night, but are not expected to fall below mid-single figures in the daytime during the chilly spell.
Pensioners and people with underlying health conditions have been urged to keep their heating on at least 18C, while people should stay warm and look out for those who are most vulnerable in cold conditions.
Dr Agostinho Sousa, consultant in public health medicine at UKHSA, said: “Cold weather can have serious consequences for health, with older people and those with heart or lung conditions particularly at risk.
“It’s important to check in on family, friends and relatives who are more vulnerable to the cold weather. If you have a pre-existing medical condition or are over the age of 65, it is important to try and heat your home to at least 18C if you can.”
David Oliver, a deputy chief forecaster at the Met Office, said: “From Sunday and into early next week an area of high pressure will dominate the UK’s weather.
“This will bring some cold nights with a widespread frost across the country. However, by day temperatures will recover to around mid-single figures, near normal for the time of year.”
Met Office meteorologist Dan Stroud added: “We are expecting a cold front to sink south during the course of Saturday and it is going to really help clear the clouds.
“It is going to allow overnight temperatures to dip below zero and we are likely to see an increasing risk of overnight frost as we move into the early part of next week.
“Wrap up warm and close your curtains in the evening to help keep in the heat.
“Daytime temperatures will be responding to the sunshine… we are likely to see them go to about average or just below average.”
The UKHSA said if people can’t heat all the rooms they use, they should heat the living room during the day and the bedroom just before going to sleep.
People should wear several layers of thinner clothing rather than one thick jumper, it added.