South-east England remains under a level three alert
The heatwave warning has been raised to "level three" by the Met Office for south-west England and the West Midlands.
The move brings those regions in line with the South East and London, where level three warnings remain in place.
The warning alerts healthcare services to help those in high-risk groups such as the elderly and young children.
Wednesday was the hottest day of the year, with 32.2C (89.9F) recorded at Hampton in south-west London.
Hot weather poses a real danger to health.
The very elderly and the seriously ill are most at risk
but people at the peak of physical fitness can still
succumb, particularly if they are under extreme
The main threat is dehydration - as we overheat we can
soon lose more fluid than we take in.
The body can no longer cool itself and our core
temperature, which should be a stable 37C, rises.
At 40C the cells inside the body begin to break down and
the body starts to malfunction.
It even stops being able to sweat, leading to more
The heart rate and breathing rate speed up and the
person may fit, hallucinate or become unconscious.
Heatstroke is a medical emergency that needs urgent
Meanwhile, firefighters in south London have been tackling a grass fire in an area the size of about four football pitches on Mitcham Common.
Level three alerts are triggered when threshold temperatures have been reached for one day and the following night, and the forecast for the next day has a greater than 90% confidence level that the day threshold temperature will again be met.
The threshold temperature for south-west England and the West Midlands is 30C (86F), while for the South East and London it is 31C (87.8F) and 32C (89.6F) respectively.
Level two warnings are currently in place for the east of England, East Midlands and Yorkshire and the Humber. These alerts are triggered by a 60% or higher chance of the threshold temperature again being reached on the second day.
North-east and north-west England are under a level one warning - the minimum state of vigilance.
Scotland, Wales and Northern Ireland are not included in the alert system.
It is the UK's first prolonged heatwave since 2006, with six consecutive days of temperatures above 30C (86F).
Ambulance services across England have reported an increase in call-outs since the hot weather began.
Some sought respite from the heat in the Appearing Rooms fountain, by Danish artist Jeppe Hein, on London's Southbank
The North East Ambulance Service NHS Foundation Trust said it would usually expect 700 calls a day at this time of year but was receiving up to 1,250.
A number of these were to beaches and rivers for heat-related illnesses and other health problems, it added.
London Ambulance Service NHS Trust said it was receiving about 5,500 calls day - up by a thousand on last year.
It said heat-related call-outs included those for breathing difficulties, fainting, palpitations and alcohol-related incidents.
The warm weather is set to continue into next week with temperatures in the high 20Cs at the weekend before rising to 30C (86F) and beyond next week - bringing with it an increased risk of thunderstorms.
Public Health England (PHE) officials have advised people to stay cool, drink lots of cold fluids and keep an eye on those they know to be at risk.
Professor Virginia Murray, head of extreme events at PHE, said: "A level three watch means take action. For us, summer is wonderful... but the real concern is that we are not used to heat in this country. We are not aware of the risks. So PHE has a heatwave plan for England which was published for this summer."
She told BBC Radio 4's Today programme that the plan was particularly targeted at healthcare providers, though there was advice for individuals.
She said: "The most important advice is to stay cool yourself, drink plenty of cool drinks - but look out for others, take care of the most vulnerable, take care of those who are very young, the elderly, those with chronic illnesses who may be particularly vulnerable to the heat and really to protect those as far as we can and to make sure we reduce the health impacts on them and the possible worrying level of increased deaths."
Prof Murray warned that many people would be reluctant to change their behaviour in response to the warm weather, which is why guidance for care homes was important.
Mike Tipton, professor of human physiology at the University of Portsmouth, told BBC Radio 5 live that signs that someone is suffering as a result of the heat should be evident.
He said: "As soon as people start to feel anything like light-headedness, feel that they're hyperventilating, if they've got a very rapid pulse, if they start to feel pins and needles in the fingers and around the limbs, slightly nauseous maybe, headaches, then really they need to stop any activity they're engaged in, move to the shade, sit down or lay down, preferably get help as well."
Jonathan McShane, from the Local Government Association, said councils are doing their bit to tend to those who may need extra assistance.
On BBC radio 5 live, he said: "Social workers, care workers, people who deliver 'meals on wheels', as part of their daily routine they're now doing an additional check to ensure that people are coping in the heat and they're staying hydrated and giving them some advice about how they can stay well and comfortable in the extreme weather."
Meanwhile, a four-week-old baby has been treated for severe sunburn at Queen Victoria Hospital in East Grinstead, West Sussex.
The hospital said it had seen 10 babies and children with severe sunburn in the past four weeks.