The cancellation of hundreds of train services was caused by the record temperatures on Monday.
The UK's transport operators warned that the worst was yet to come as roads and trains were quieter than usual on Monday.
Speed limits were put in place at midday as the temperature reached a high of 30C.
The airport halted operations on Monday due to a runway issue. A surface defect was identified after the high temperatures.
The passengers on the easyJet flight from Italy to the airport were told they were being diverted because of some melting on the runway.
Passengers should only use the railway on Monday and Tuesday if absolutely necessary and be prepared for long journeys, according to Network Rail.
After England and Wales slowed down trains for safety due to higher temperatures, Scotrail followed suit. On the east coast line linking London, York and Edinburgh the top speed was halved to 60 mph.
Some of the infrastructure on the east coast line is more vulnerable to damage in heat than other parts of the railway. The line will not be open on Tuesday.
There was one train an hour on the west coast mainline on Monday, with a London-Manchester service taking three and a half hours.
Passengers who travel on Monday should not be lulled into a false sense of security, as the speed limits only come into effect at noon, according to a Network Rail spokesman.
The restrictions will stay in place until the end of Tuesday because of the high temperatures.
Suburban trains rarely exceed 90mph, so long-distance services will inevitably be disrupted. Break downs are inevitable with peak temperatures of about 40C forecast by the afternoon and steel rails and equipment likely to be 20 C hotter.
Damage to the infrastructure over the next two days could affect services on Wednesday when temperatures are predicted to plummet.
There were noticeably fewer passengers reported at the stations on Monday. The passenger numbers were down.
According to Transport for London, passenger numbers on the tube and bus were 18% and 10% lower, respectively. Travelers were advised to travel only if essential, with temporary speed restrictions liable to slow and disrupt the network.
Parts of the London Overground were suspended because of the heat.
The data from the satnav firm showed a decrease in the number of cars on the road. The morning rush hour in London, Bristol, Glasgow and Manchester was less congested than it was a week ago.
Motoring organizations warn of a high risk of breakdown due to overheating engines, tire failures and faster fuel consumption in the heat.
There were no reported problems with the main strategic roads being impervious to temperatures of more than 60C.