Video report by ITV News Correspondent Emily Morgan
Forecasters said the temperature record for July had already been broken with 37.7C at Kew Gardens, London and in Writtle, Essex - both topping the previous high for the month of 36.7C set at Heathrow in July 2015.
The temperature hasn't quite heated up enough to break the all-time UK record of 38.5C recorded in Faversham, Kent, in August 2003.
Sunbathers and swimmers have settled on beaches and queued outside lidos to make the most of the sunshine across the country.
But the scorching conditions may spark thunderstorms - and commuters were hit by a raft of rail delays and cancellations;.
The extreme heat has caused damage to overhead electric wires between London St Pancras and Luton, blocking all lines.
This is affecting East Midlands Trains and Thameslink services. East Midlands Trains posted a message on Twitter urging passengers "DO NOT TRAVEL" and warned it had been unable to secure ticket acceptance via alternative routes.
Thameslink said "you are strongly advised not to travel", and said journey times will be extended by up to 90 minutes.
Overhead electric wires between London Euston and Watford Junction have also been damaged by the heat, disrupting Virgin Trains services.
A fire by the tracks in north London
A yellow weather warning is in force for most of England, except the south-west, and parts of Scotland from 3pm on Thursday until 4am on Friday.
“It will get into the 30s across the country and reach the mid-30s in the south-east,” Met Office meteorologist Greg Dewhurst said.
Lightning storms have already caused fires and rail disruption this week during the heatwave.
Network Rail warned speed restrictions may be introduced in areas where tracks are at risk of buckling.
Extreme weather action teams (EWATs) have been “activated” to keep passengers safe and trains running, it said.
The top ten temperatures recorded in the UK before today:
38.5 C, August 10, 2003
37.1 C, August 3, 1990
36.7 C, July 1, 2015
36.7 C, August 9, 1911
36.6 C, August 2, 1990
36.5 C, July 19, 2006
36.4 C, August 6 2003
36.1 C, August 4, 1990
36.0 C, August 9, 2003
35.9 C, July 3, 1976
The Rail Delivery Group, which represents the industry, advised passengers in London and the South East to consider changing their travel plans on Thursday owing to the heat.
London North Eastern Railway (LNER), which runs inter-city services on the East Coast Main Line, is advising customers against travelling on Thursday.
It said some services were likely to be cancelled or delayed as speed restrictions will be imposed between Peterborough and London King’s Cross.
What a thermal camera shows on the London Underground
The Met Office has warned heatwaves are on the increase as a result of climate change.
It was even possible the mercury could have climbed to 40C, which would be “unprecedented” for the UK climate, weather forecasters said.
The scorching temperatures gripping the UK and much of Europe come against a backdrop of global warming of 1C since the Industrial Revolution driven by greenhouse gas emissions.
Both Belgium and the Netherlands broke their all-time maximum temperature records on Wednesday, reaching 39.9C and 39.1C respectively, the Met Office said.
Higher temperatures are making extreme hot spells more likely and more intense, experts warn.