A level 3 "heatwave action" heat-health alert has been declared for all parts of England, meaning there is a 90% probability of heatwave conditions.
Public Health England advised avoiding the sun between 11:00 and 15:00 BST.
Wimbledon spectators - who have been covering their heads with umbrellas, newspapers and towels - have been advised to wear hats.
The centre court roof has been closed to protect the playing surface from the heat and is due to reopen at 11.30.
The weather is very different in Scotland, where forecasters have warned of thunderstorms, torrential downpours and hail stones up to 1cm in size.
In England, Network Rail instructed train companies to slow down at vulnerable locations where tracks could buckle because of the heat.
Affected routes include Abellio Greater Anglia trains between London Liverpool Street and Ipswich and First Great Western services between London Paddington to Bourne End and Henley-on-Thames
Virgin`s East Coast line between Leeds and London Kings Cross is also running a reduced service
Commuters have been advised to check their journeys before travelling and to carry water and sunscreen
Health warnings have also been issued to young children, the elderly and those with serious illnesses who are encouraged to stay in the shade, wear loose clothing and drink plenty of water.
Vicky Barber from the British Lung Foundation Helpline said: "During hot weather, the air we breathe has lower moisture levels than usual, which can have a drying effect on our airways. As a result, people with respiratory conditions such as COPD or severe asthma may find it harder to breathe, feel more tired, or find their lungs feeling heavy or tight."
Dr Angie Bone, head of extreme events at Public Health England, said: "Employers should ensure indoor areas are kept cool and consider allowing these individuals to travel to or from their place of work during cooler, or less busy times of the day.
"For those working or exercising outdoors, strenuous physical exertion during the hottest part of the day should be kept to a minimum."
Some schools have cancelled their sports days, including Castledon School in Wickford, Essex, and Christchurch Primary School in Ilford, north-east London.
One animal at the Cornish Seal Sanctuary has been making the most of the sunshine.
Pumpkin, a grey seal, has learned to jump on the sun canopy over his pool, which he uses as a hammock as he rolls around sunbathing.
He learned the trick in May but has been doing it every day recently because of the hot weather.
Hot weather can be fatal for many animals, and the RSPCA has reminded people never to leave a dog alone in a car on a warm day, even with the windows left open.
The PDSA has advised that pets should always have access to shade, and hutches should not be left in direct sunlight.
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