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Temperatures are set to rise over the coming days after an amber weather warning came into force at midnight.
The Met Office has warned of travel disruption and that lives could be at risk as temperatures are expected to rise further.
The bureau has issued its first red weather warning for extreme heat as parts of the county are predicted to reach nearly 40C - a new UK record - next week.
Meanwhile, an amber weather warning is currently in force across Kent, meaning people could suffer serious illness or danger to life.
The Met Office has forecast dry weather as temperatures jump to 31C in most places.
The government's advice is that 999 services should be used in emergencies only and people should seek advice from 111 if they need non-emergency health advice.
Substantial changes in working practices and daily routines are likely to be required and delays on roads are possible, the Met Office says.
Travel delays are expected, with train operator Southeastern warning services could be disrupted and advising people they should only travel if necessary.
Passengers have been advised to check the status of their journey before travelling and ensure they are well-prepared for extreme conditions.
Kent Highways has urged people to be prepared by checking the latest travel updates, leaving more time for journeys, checking vehicles,
Saturday kick-started the beginning of the heatwave, with Heathrow Airport and Kew Gardens, in west London, recording the highest temperature of 29.1C.
The warm weather saw increased demand for water in some parts, with South East Water confirming residents in Challock and Molash having no water due to “continuous hot weather and significantly increased demand for water” putting “significant pressure on our network”.
A statement from the supplier said: “We’re continuing to work on restoring your supplies, and will continue to work on this overnight.
“As a precaution, we’re going to open up the bottled water station at Challock Village Hall tomorrow morning, at 8am.
“The team will be there until 7pm tomorrow night.”
Meteorologists have given an 80% chance of the mercury topping the UK’s record temperature of 38.7C, set in Cambridge in 2019, with the current heatwave set to peak on Tuesday.
Temperatures are forecast to increase by several more degrees on Tuesday – up to the mid-30s for much of England and Wales.
Cabinet Office Minister Kit Malthouse warned transport services face “significant disruption” next week due to the heatwave, urging people not to travel.
Ministers held an emergency Cobra meeting yesterday after meteorologists warned of record high temperatures in England next week that could put lives at risk.
After chairing the meeting, Mr Malthouse told the BBC: “Obviously the transport providers are messaging people that they should only travel if they really need to on Monday and Tuesday.
“Services are going to be significantly affected. The heat will affect rails, for example, so the trains have to run slower. There may be fewer services. People need to be on their guard for disruption.
“If they don’t have to travel, this may be a moment to work from home.”
Mr Malthouse said steps have been taken to ensure hospitals and ambulances that may come under pressure were prepared, while schools were being issued with guidance to enable them to remain open.
He added in a separate statement: “It’s important that we all continue to follow public health advice to keep cool, and take simple precautions like drinking lots of water and seeking shade, and also checking on vulnerable friends and neighbours.”
The UK Health Security Agency has increased its heat health warning from level three to level four – a “national emergency”.
Level four is reached “when a heatwave is so severe and/or prolonged that its effects extend outside the health and social care system… At this level, illness and death may occur among the fit and healthy, and not just in high-risk groups,” it said.