There a huge speed restriction in place today on trains from Leeds to London due to the hot weather.
Passengers who want to travel from Leeds to London are being advised not to as steel railway tracks are becoming too hot, which may cause them to buckle under the pressure.
Speed restrictions have therefore been imposed on journeys across the country.
The speed limit of the East Coast Main Line is 125mph in normal circumstances.
But the extreme weather is set to see that limit reduced to 60mph at the southern end of the line.
This means there will be fewer services and busier trains on the main routes into and out of London - including the LNER Leeds to London line.
In particular, a speed restriction between London King's Cross and Peterborough will be in place on Thursday, July 25 - when temperatures are set to reach the high 30s.
There will also be a reduced timetable and they expect services to be "extremely busy."
Passengers have been encouraged to avoid all travel.
A spokesperson for LNER said: "We are expecting some very high temperatures across the UK tomorrow. As a result, a speed restriction will be in place between London King’s Cross and Peterborough all day.
"LNER will be running a reduced timetable on Thursday 25th July and we expect our services to be extremely busy. We would encourage customers to avoid travel tomorrow where possible.
"Your tickets dated for travel on Thursday 25th July, will be valid for travel on Friday 26th July, Saturday 27th July and Sunday 28th July.
"If you choose not to travel, you will be entitled to a full refund. Please check before you travel and click here for the latest information."
Network Rail said the restrictions have been put in place to protest passenger safety in these "unprecedented conditions."
Rob McIntosh, Managing Director of Network Rail Eastern, said: “Passenger safety will always be our number one priority. And with forecasts of unprecedented temperatures, we have to take action to keep people safe.
“Reducing speed limits will mean fewer services and busier trains on our main routes into and out of London.
“So I’d like to ask all passengers to think about whether their journey is really necessary and, if it is, to make sure they plan well ahead.
“I’m sorry for the disruption this will cause, but it is essential to maintain the safety of the travelling public.”
The restrictions are set to lead to train cancellations, longer journey times and busier services on the network.