Great Northern and Thameslink will not be running a full service due to Network Rail imposing speed restrictions, with changes expected to affect the Bedford to London line, routes in the capital, and the London to Brighton line.
The changes are due to the extreme heat currently forecast for Tuesday, and the "possible risk to safety through potential damage to the track and power".
Thameslink states: "On Monday and Tuesday, only travel if your journey is absolutely necessary.
"The Met Office have issued a 'Red Warning for Extreme Heat'; this means there is a substantial risk of disruption to the train service."
Great Northern and Thameslink are asking commuters to be aware of the following changes:
On Tuesday, you cannot travel on Great Northern or Thameslink routes to or from London Kings Cross or Moorgate. There will be no trains on these routes for the whole day. Network Rail is advising that you Do Not Travel in the area.
Thameslink and Great Northern will be running a significantly reduced service across all routes. On Tuesday there will be no service on routes to or from London Kings Cross or Moorgate.
Southern services are expected to mostly run as planned but some routes see the service reduced
Gatwick Express services will not run
Other train operators are also affected in the same way and are also advising you only to travel if absolutely necessary
All trains will be delayed by speed restrictions with cancellations expected and a high chance of incidents affecting trains that are still planned to run.
Even if you are able to travel in the morning on Monday and Tuesday, you may find there is significant disruption to return journeys in the evening, so if you must travel then you should consider alternative ways to get home.
Thameslink states: "We are strongly advising that you should only be travelling if your journey is absolutely essential. Journey planners for Monday will be updated on Sunday, and Tuesday will be updated on Monday. We are still working on the detail of our revised service."
At this time it anticipates the following changes:
North of London:
A train shuttle will run between Cambridge and Kings Lynn, this will mean a change of trains at Cambridge for journeys through to London
There will be a very reduced service between Cambridge and London, a stopping service only.
Services between Moorgate and Stevenage / Welwyn Garden City will be reduced, with 2 trains per hour on each route
Peterborough / Horsham services will only run between Peterborough and London Kings Cross
There will be no services between Finsbury Park and St Pancras, meaning no peak services between Sevenoaks, London and Welwyn Garden City
TUESDAY ONLY - Peterborough, Kings Lynn, Cambridge, London and Great Northern Suburban area.
You cannot travel in this area - There will be no trains on any routes to or from London Kings Cross or Moorgate on Tuesday
A train shuttle is expected to run between Cambridge and Kings Lynn, but this will be the only service in the area on Tuesday
Monday and Tuesday - Bedford and London
Bedford to London services will be reduced to 2 trains per hour
Luton to Rainham services will run, stopping at all stations between Luton and London
St Albans to Wimbledon / Sutton services will be suspended throughout
There will be no peak Thameslink services to or from Orpington
South of London:
Monday and Tuesday - Thameslink Services
There will be no Thameslink service between Sutton and London, either via Mitcham Junction or Wimbledon.
There will be 2 Thameslink trains per hour between London, Gatwick, and Brighton (not calling at Redhill)
Thameslink services between Horsham and London will be amended to run between Horsham and Redhill only. Customers will need to use Southern services between Reigate and London Victoria for onward journeys.
There will be no Thameslink service to/from East Grinstead, Orpington or Littlehampton.
Thameslink services will run between Blackfriars and Sevenoaks only.
Monday and Tuesday - Southern Services
Southern services between East Croydon and London Bridge via New Cross Gate will not run.
Southern services between Caterham and London Bridge via Tulse Hill will not run.
Streatham station will have no service.
Gatwick Express services will not run. 1 Southern train per hour will run between Brighton and London Victoria.
Thameslink states: "If you do travel, you should carry a bottle of water. Do not board a train if you feel unwell, seek help at the station or use a help point. Avoid using the emergency alarm on the train between stations, as this can cause a delay in help reaching you.
"If you decide not to travel, you can use tickets dated Monday 18 and Tuesday 19 July to travel with Southern, Gatwick Express, Thameslink or Great Northern on Wednesday 20 and Thursday 21 July instead. If you choose to delay your travel, please note that the original ticket restrictions will still apply. If you are using an Advance Purchase ticket, please travel as close to the original departure time as possible. Please check with all train companies you intend to travel with in case their arrangements differ.
"If you purchased a ticket with us at one of our ticket offices, or on our website and you have been unable to complete your journey as your train is cancelled, you can apply for a refund. If you bought your ticket with us, simply return your unused ticket to a Southern, Gatwick Express, Thameslink or a Great Northern ticket office (unless it's an E-ticket) or apply using our online refund form. You will not be charged the £10 admin fee.
"Please note this only applies to single or return tickets, for details on season tickets please see our website.
"If you purchased your ticket from another train company's ticket office, or via another online retailer then please contact them directly to discuss the options available to you."
It added: "For Monday 18 and Tuesday 19 July, if Season Ticket & Flexi Ticket holders are unable to travel or chose not to travel, you can claim compensation through our Delay Repay scheme.
"This only applies to monthly and longer season ticket holders. Flexi ticket holders must have activated a days' worth of travel. You should make one claim for each day affected claiming a delay of 120+ minutes which will provide you with the value of one days' travel.
"You need to apply for compensation online within 28 days of the intended travel date."
Journeys for July 18 and 19 are showing in the National Rail Enquiries real-time Journey Planner. If you would like to follow this incident on Twitter, please use #GTRweather
Thameslink states: "You may be entitled to compensation if you experience a delay in completing your journey today. Please keep your train ticket and make a note of your journey, as both will be required to support any claim."