The UK has recorded its second hottest day ever, with temperatures reaching 38.1C (100.6F) in Cambridge.
It breaks the previous record for the hottest day in July of 36.7C, and falls just short of the all-time high of 38.5C, reached in 2003.
Commuters faced disruption after Network Rail reported a number of heat-related incidents on the railway.
Forecasters warned the heat could lead to heavy rain in some areas, causing more disruption to travellers.
The Met Office said the temperature reading from Cambridge was only the second time the UK had gone over 100F.
Elsewhere in Europe, new high temperature records were set in France, Germany and the Netherlands.
How is it affecting travellers?
Network Rail said heat-related incidents were causing disruption across the rail network and warned people to make checks before travelling to see how their journey was affected.
It said it was working "flat out" to fix the issues as quickly as possible.
The Rail Delivery Group, which represents train operators and Network Rail, said the disruption was particularly bad in London and the South East and warned it could continue until the weekend.
Robert Nisbet, director of nations and regions at the group, said 20 out of 26 train companies had been affected by cancellations and speed restrictions.
"We believe there could be roll-on impacts tomorrow, because many of the trains will be in the wrong places, many of the rail staff will be in the wrong places and it will take time to re-set, to stabilise the timetable again," he said.
Commuters became stuck at St Pancras station in London after overhead wires were damaged, severely disrupting East Midlands and Thameslink services.
Boards displayed at the station announced most trains had been cancelled, with others delayed.
Damaged wires also led to travellers facing delays and cancellations to journeys between London Euston and Watford Junction.
East Midlands Trains advised passengers not to travel on some of its train services, while Great Western cancelled some trains between London, Cardiff and Swansea, with routes between London and Scotland also affected.
Delays and cancellations are also expected for journeys across the Gatwick Express, Great Northern, Southern and Thameslink networks until the end of Thursday.
Southeastern Railway also warned customers to avoid all but "absolutely necessary" travel.
What's the forecast?
On Thursday, Scotland recorded its hottest day of the year at 31C, while in Wales it was forecast to exceed 30C. A weather front close to Northern Ireland will keep it cooler.
Later on Thursday, eastern Scotland and the north and east of England could see rain, with a Met Office yellow warning for thunderstorms into early Friday morning.
There are warnings that the storms could trigger travel delays, flash flooding, and power cuts.
Heatwave hits Europe
On the continent, the heat rose above 40C in France, Germany and the Netherlands, breaking records.
Paris saw a record high temperature of 42.6C and French reports suggest five deaths might have been linked to the heatwave.
In parts of northern Germany, rivers and lakes have dried up, bringing warnings that fish could be "severely threatened".
How to stay safe
People are being urged to help out vulnerable friends, relatives and strangers in the heat.
Age UK has issued guidance for older people to stay safe while homeless charities are handing out water and sun cream.
Public Health England has maintained a level three heat health watch for eastern areas of England.
In Bristol, thousands of people were left without water for more than 10 hours after a water main burst, with Bristol Water saying the problem might have been caused by the heat.
Homeless charities have handed out water and sun cream to rough sleepers across the country and Public Health England issued a level-three heat health watch for eastern areas of England.
Britain is not used to such extreme temperatures, which means some people could be vulnerable to heat exhaustion.
The NHS recommends keeping all babies under six months out of direct sunlight, and older infants should be kept out of the sun as much as possible.
They should be kept in the shade or under a sunshade if they're in a buggy or pushchair. Sun cream with a high sun protection factor should be applied regularly - particularly if children go into water.
All children should be given plenty of fluids and the NHS says babies who are being breastfed may want to feed more than usual, but will not need water as well as breast milk.
NHS advice also says people should cool off immediately if they show the following symptoms: headaches, feeling dizzy, loss of appetite, nausea, excessive sweating, cramps, fast breathing and intense thirst.
For more information on how to keep safe in the heat, read:
Is the heatwave caused by climate change?
While extreme weather events like heatwaves occur naturally, "research shows that with climate change they are likely to become more common, perhaps occurring as regularly as every other year", the Met Office says.
It conducted a study last year that found that the UK was now 30 times more likely to experience heatwaves compared with the year 1750, because of "the higher concentration of carbon dioxide (a greenhouse gas) in the atmosphere".
Records going back to the late 19th Century show that the average temperature of the Earth's surface has increased by about one degree since industrialisation.
A climatology institute in Potsdam, Germany, says Europe's five hottest summers since 1500 have all been in the 21st Century.
Scientists are concerned that rapid warming linked to use of fossil fuels has serious implications for the stability of the planet's climate.
What are the UK's current record temperatures?
The current record temperatures across the UK are:
- England and UK: 38.5C (101.3F) in Faversham, Kent on 10 August 2003
- Scotland: 32.9C (91.2F) in Greycrook, Borders on 9 August 2003
- Wales: 35.2C (95.4F) in Harwarden Bridge, Flintshire on 2 August 1990
- Northern Ireland: 30.8C (87.4F) in Knockarevan, County Fermanagh on 20 June 1976 and Shaw's Bridge, Belfast on 12 July 1983