Given the expected high temperatures and weather warnings issued by government, rail operators are urging customers to stay indoors and keep cool.
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Level four comes with a warning that illness and death may occur - even among the fit and healthy.
Network Rail has called on all passengers to only travel where absolutely necessary while Northern, TransPennine and LNER have cancelled a number of services.
Steve Hopkinson, operations director for Network Rail, said: “Our railway is simply not engineered to run normally in such extreme temperatures. We’ve got extra teams out around the route, ready to respond to incidents but with temperatures set to break records, we need to also reduce the speed at which trains can run throughout Monday and Tuesday.
"This reduces the risk of tracks buckling in the heat and also means that when the overhead line expands it won’t create a safety risk to trains."
If passengers absolutely must travel, they should keep up to date with the latest information via National Rail Enquiries or with their train operator.
Northern's regional director Tony Baxter said the network don't issue 'do not travel' notices lightly.
“We don’t issue ‘Do Not Travel’ notices lightly, but given the guidance published by government and expected disruption caused by extreme temperatures, we feel this is the safest advice for our customers," he said.
“There will be blanket speed reductions in place and a limited timetable in operation throughout the region.”
Northern’s announcement follows Network Rail’s decision to close the East Coast Main Line (ECML) between 12pm and 8pm for all locations between London King’s Cross and York and Leeds due to the extreme weather.
No LNER trains will run between Leeds and London King's Cross on Tuesday with temperatures due to hit as high as 38 °C.
TransPennine Express have also advised passengers that an amended timetable will be in operation across both days.
Anyone making an essential journey is urged to:
Carry a bottle of water to keep hydrated.
If waiting at a station, try and find a safe spot in the shade.
If you do have to go into the sun, apply some suncream and wear a hat.
If you start to feel ill; do not board the train, speak to a member of staff or use the help point at the station.