Services run by GWR, Heathrow Express and the Elizabeth line are affected after the fault at Hayes & Harlington.
The lines between Reading and Newbury are also closed due to a person being hit by a train.
GWR trains are to be diverted, delaying journeys to the capital until at least 10am just an hour before the Queen’s state funeral begins in Westminster Abbey.
GWR urged mourners looking to follow the Queen’s journey to Windsor to travel from Waterloo to Windsor & Eton Riverside.
A spokesman said: “We are very sorry for the disruption this morning and are working hard to get services resumed as soon as possible.”
The Elizabeth line is part suspended between Paddington and Reading.
There are fears the transport network will be overwhelmed on Monday afternoon if too many people visiting the capital travel home immediately after the funeral procession leaves Westminster shortly after noon.
TfL boss Andy Byford told the PA news agency: “We’re ready for probably one of the busiest days Transport for London has ever faced.“It’s hard to say exactly how many additional people (will travel), but we’re preparing for potentially a million people just within the footprint of the royal palaces and Hyde Park.”
Mr Byford said TfL is “leaving nothing to chance”, with non-essential meetings postponed and people from across the organisation working to ensure visitors can “get around the city”.
Network Rail chairman Sir Peter Hendy warned that trains will be “extremely busy”.
He said: “This is the biggest public transport operation since the London 2012 Olympic and Paralympic Games, and we’re working closely with all train operators to run extra trains through the day and into the night.
“To help us provide the best possible experience and avoid lengthy queues at stations we’re asking people not to rush home after the funeral and the processions, but to take their time and experience London on this memorable day.”
Network Rail has postponed engineering work and is keeping its London stations open overnight to provide shelter for mourners struggling to get home.
All-night trains are only serving limited destinations, mostly within the M25.
Stationary trains are being used as waiting areas in the early hours of the morning for people waiting to catch a train home.Priority will be given to elderly and vulnerable mourners.
Three Tube stations – Westminster, St James’s Park and Hyde Park Corner – will be closed for most of Monday morning to avoid being overcrowded.
More than 100 Heathrow Airport flights will be cancelled to prevent aircraft noise disturbing proceedings at Westminster Abbey and Windsor Castle.
The west London airport announced that 15% of its 1,200 flights due to take off or land on Monday will be disrupted.British Airways – the most-affected airline – cancelled 100 short-haul flights due to the restrictions.