The number of deaths in France linked to the searing heatwave has climbed to four toddlers and more than 55 drownings, as the brutally hot conditions sweeping Europe were forecast to shift east, choking 150 million people under 35C (95F) temperatures.

Scientists said the heatwave was the most severe and widespread ever, leaving nearly half of the region’s 850 largest cities grappling with unprecedented heat stress. The extreme temperatures were made possible by the climate crisis driven by fossil fuel burning, they said.

On Friday, a hospital in Marseille said an 18-month-old child had died earlier in the week in emergency care after he was found in a car in a state of hyperthermia. A police source told the newspaper Le Figaro it was believed that the father, who works in the area, may have forgotten his son in the car when he was supposed to drop him off at daycare.

Earlier this week a three-year-old boy in a Paris suburb was found dead after climbing into a car and becoming trapped when the child lock was activated, while the bodies of two children, aged two and four, were found in their family’s car in a residential parking lot.

Earlier in the day, France’s sports minister, Marina Ferrari, said at least 55 people across the country had drowned – up from the 40 reported earlier in the week. “By yesterday night we were at 55, but we fear that the situation may worsen,” she told the broadcaster Franceinfo.

In the UK, the Met Office said the record for hottest June day had been broken for the third day running. Provisional figures showed a temperature of 37.3C in Santon Downham, Suffolk, on Friday, beating the previous record of 36.7C set on Thursday. “And temperatures are still rising,” it added.

As a Met Office red alert for heat remained in place for an unprecedented third day running for London and south-east England, while an amber alert covered most of central and eastern England, calls on the government to take more action grew louder.

The UK Health Security Agency’s red heat-health alert has been extended until 11pm on Friday and covers all of southern and central England, with an amber heat-health alert issued for all of England until 9am on Sunday. A red alert means there is a significant risk to life even for healthy people. Several hospitals have declared critical incidents, as health experts warned emergency services were struggling to cope with the impacts of the heatwave.

More than 1,000 schools in the UK have been closed or partially shut this week as poorly insulated buildings, many without air conditioning, overheated. Train passengers were urged to avoid non-essential travel on Friday, with many railway operators running reduced or slower services. Firefighters continued to tackle a wildfire in Derbyshire affecting an area of about 200 hectares (494 acres).

A hosepipe ban in Kent came into effect on Friday morning as South East Water said demand had increased in response to the heat, while late on Thursday Britain’s energy operator raised the alarm over power supplies needed to meet the extra demand for air conditioning and fans.

London ambulance service said it had responded to its highest number of life-threatening emergencies ever on Wednesday, with its chief operating officer, Craig Harman, adding that he expected “demand to grow day on day over the next couple of days”.

Officials in Paris, where temperatures hit a June record of 40.9C on Wednesday, expressed similar concerns. “We are reaching a saturation point in hospital facilities,” the Paris police chief, Patrice Faure, told BFM TV as he announced a ban on drinking takeaway alcohol in the street.

The head of the Association of French Emergency Doctors said there had been 55 deaths in the care of emergency health services in Paris in 24 hours. “Fifty-five is enormous,” Patrick Pelloux told Reuters. “Normally it’s three or four over 24 hours.”

Organisers of Paris Pride said they would postpone the event, probably until September, after police expressed concerns that the thousands of attenders could increase pressure on emergency services. The Pride march in Lyon as well as the Solidays music festival – aimed at raising funds to support programmes for people affected by HIV – were also called off.

While the extreme temperatures were forecast to peak in France and Britain on Friday, the heat was expected to intensify in central and eastern Europe.

In Belgium, a planned re-enactment of the 1815 Battle of Waterloo, which regularly draws thousands of people, was cancelled, while organisers in the Netherlands – where officials this week issued their first-ever red alert for heat – cancelled the four-day techno music festival Defqon 1.

Budapest Pride, which last year emerged as a symbol of resistance against the rightwing crackdown on LGBTQ+ rights, said it would go ahead as planned on Saturday, despite officials issuing the highest level of heat alert. Instead organisers asked vulnerable people to “support us from home” rather than attend in person.

On Friday parts of the Balkans were bracing for temperatures to climb up to 39C, as were parts of Austria, where the national rail company warned that train tracks ‌could buckle in the coming days. Germany, where extreme heat had already caused the surface of the A2 motorway to buckle and rupture over several lanes on Thursday, was expecting highs of about 40C.

Further east the brutally hot conditions were, for once, not the order of the day.

Although temperatures were in the upper 30s in Greece and Cyprus, the heat was relieved by early Etesian winds, the northerly breeze that brings respite to the region every summer. In a far cry from scenes in major European capitals to the west, heavy rainfall, storms and even hail were predicted across parts of central Greece late on Friday.

Spared of the humidity that heightened mercury levels so often bring, tourists could be seen ambling comfortably around the ruins of downtown Athens – an ease shared by authorities that have yet to announce the heat alerts seen in western Europe.

In countries more usually on the frontline of the climate emergency – with the Mediterranean warming 20% faster than the global average – temperatures are not expected to exceed 40C until mid-July. Once they arrive, weather forecasters are predicting the start of an exceedingly hot two months with scorching days and nights.

John Kennedy, the World Meteorological Organization’s climate information chief, said Europe had warmed by about 2C in the 50 years since the heatwave of 1976.

“Heatwaves like this are what we expect to see in a changing climate,” he said. “Extreme heat will occur more frequently, for longer duration and with greater intensity as global warming continues.”