Temperatures hit 35C (95F) on Thursday, making it the hottest day of the year so far.
The new high was recorded at Heathrow Airport and the Met Office said it was trying to confirm if Wisley in Surrey recorded 35.1C.
As people packed beaches and parks, many travellers used social media to complain of inadequate ventilation and air conditioning on trains.
Holidaymakers hoping to speedily get to France on the Eurotunnel endured delays of five hours – some much longer – as they queued in their cars to get on a train.
The company tweeted that “unprecedented high temperatures” were “affecting the operation of air conditioning on our shuttles”.
Amid tinderbox conditions, 56 fires were reported on grass verges next to England’s motorways and a combine harvester caught alight in Nottinghamshire, scorching a field.
Some NHS trusts were also reporting “winter conditions” in terms of patient numbers.
“Some trusts are reporting record numbers of people coming into A&E, with increased emergency admissions, often for respiratory problems and conditions made worse by dehydration,” said Saffron Cordery, deputy chief executive of NHS Providers.
On Friday, the heat is predicted to become more intense – and could potentially surpass the UK’s all-time record.
“Furnace Friday” – as one newspaper has termed it – may topple the 38.5C (101.3F) recorded in Faversham in Kent in August 2003.
Overnight temperatures nearly everywhere will at least be in the high teens, with thundery showers affecting parts of the Midlands and North East England in the early hours.
A sweltering 37C (98.6F) is forecast for the South East and East Anglia, with the storms returning in the mid-afternoon and evening as the heat builds.
The Met Office has issued a yellow warning for torrential rain for eastern areas, and said there could be lightning, large hail stones and localised flooding.
The evening rush hour could see treacherous conditions in some areas.
MPs have warned that heat-related deaths will treble by the middle of the century unless the government takes action.