The Met Office has issued a yellow health warning for heatwave conditions from Tuesday until Thursday evening.
The warning means there is an 80% chance of temperatures which could be a risk to health, and is intended to help social and healthcare teams prepare.
Fears that railway tracks could buckle in the heat prompted Network Rail to introduce speed restrictions.
The hot weather is expected to last until the weekend, when temperatures will slowly drop off.
The Met Office said heatwaves can be dangerous for the very young, the elderly or those with chronic disease.
The yellow health warning, covering the west and north-east of England, refers to conditions between 09:00 on Tuesday and 18:00 BST on Thursday.
- Ice creams, hot dogs and a weatherman in shorts
Met Office forecaster Mark Foster said: “High pressure is going to dominate this week so we can expect very high levels of pollen and UV.”
On Monday the highest temperature of 30.1C was recorded at Hampton waterworks in west London.
The year’s previous record temperature had been 29.1C in April at St James’s Park in central London.
In Scotland, the highest temperature of 26.7C was recorded in Balmoral, while the same temperature was also reached in Castlederg, Northern Ireland.
Temperatures reached 28.7C in Usk, in south-east Wales.
BBC Weather presenter Matt Taylor said Monday’s high temperatures were likely “to be beaten in the coming week”.
“If Scotland and Northern Ireland get above 29C, which they are likely to do by the end of Wednesday, it will be the hottest June day in both countries since 1995.”
“The heat lasts to the end of the working week and then slowly drops off at the weekend.”
He explained that the jet stream looping to the north of the UK, and then back down to eastern Europe, has created an area of high pressure over the country which is not shifting.
However, for Greece, the direction of the jet stream has produced very stormy conditions.
Network Rail said track temperatures could reach as much as 20C above the air temperature, meaning the steel rails can expand markedly. The reduced speeds are intended to lower the force exerted on the track, reducing the risk of buckling.
One route affected by the speed limits is the line between London Waterloo and New Malden, in south-west London, where trains will be slowed after 11:00 each day until Friday.
Andy Thomas, managing director of England and Wales at Network Rail, said: “Our engineers and specialist extreme weather teams are monitoring track-side temperatures at vulnerable locations.”
The Trade Unions Congress (TUC) has urged bosses to ensure staff working outdoors are protected from the hot weather.
TUC general secretary Frances O’Grady said: “We all love to see the sunshine, but working outdoors in sweltering conditions can be unbearable and dangerous.
“Bosses must ensure their staff are protected with regular breaks, lots of fluids, plenty of sunscreen and the right protective clothing.”
Heatwave health warnings explained
Green – minimum state of vigilance during the summer.
Yellow – Alert and readiness – Social and healthcare services are on standby to reduce harm.
Amber – Heatwave action – Care services target high-risk groups, like the elderly, with specific help. General advice is given to keep homes cool, drink plenty of fluids, and so on.
Red – National emergency – Reached when a heatwave is so severe that illness and death may occur among the fit and healthy, not just among high-risk groups.