The elderly and those with heart and respiratory problems are most at risk, says the Local Government Association (LGA).
Community wardens, social workers and council staff have been told to stay vigilant for people who might be struggling and will be making extra visits to those at risk.
A heatwave alert was issued by the Met Office on Monday, warning that temperatures would rise above 30C (86F) for at least two consecutive days and remain about 15C (59F) at night.
Forecasters say it could hit 34C or even hotter in southeastern England on Thursday and Friday.
Monday was the hottest day of the year so far, with 33.3C (91.9F) recorded in Santon Downham, Suffolk.
Izzi Seccombe, chairwoman of the LGA’s community wellbeing board, said: “Social workers, community wardens and maintenance staff are all on high alert, identifying and looking out for those who might be struggling.
“Councils are determined to reduce the toll as much as possible, but they cannot do it alone. Local people can make a massive difference by helping us identify other residents who might need some advice or practical help.
“Looking around at how our older neighbours are coping as we walk our children to school or head to the beach for a day out takes no effort, but could be crucial in making sure they are also able to make the best of the summer.”
Tips for staying cool in the heat
:: Draw the curtains in rooms facing the sun
:: Opening windows will let in a breeze, but also hot air. Open them in the evening when the temperature drops
:: Lights, TVs and other electrical devices all emit heat – turn them off and unplug if you can
:: Put a bowl of ice or a few frozen water bottles in front of your fan for extra-cold air
:: A cold, wet cloth on areas like your neck or wrists can also help lower your temperature
:: A spray bottle with water is handy to carry when out as you can get a quick cooling mist
:: Bear in mind that alcohol and drinks with caffeine can make you more dehydrated
:: Drink lots of water – take a bottle with you when travelling
:: Isotonic sports drinks are also good as they replace the minerals you lose in sweat
:: Try to keep out of the sun between 11am and 3pm
:: Wear a hat, put on sunscreen and walk in the shade
:: If possible, avoid exercise and physical exertion in the hottest part of the day
:: Light, loose-fitting cotton clothes will help keep you cool. Avoid dark-coloured garments