Four tracks have reopened but delays and cancellations are expected to continue until lunchtime.
Some services have started running out of Paddington railway station a day after trains became entangled in overhead power cables.
Four tracks reopened at 09:30 BST after engineers worked overnight but disruption is expected to continue until lunchtime, Network Rail said.
Services will also finish before 22:00 to allow further work on the lines.
People who headed to London and Windsor for the Queen’s funeral proceedings on Monday were badly hit by cancellations.
Large queues also formed at London Waterloo during the afternoon as people tried to make their way home from the capital.
The issues began at about 06:30 after one train became entangled in overhead wires. The same then happened with subsequent services passing through Hayes and Harlington station, with about two miles (3.2km) of cabling damaged.
While all four tracks are now open, overhead electric wires are only in operation on two of the lines.
The first Elizabeth line train to Heathrow since Monday morning departed Paddington at 10:17.
No trains had been able to run from Paddington station to West Drayton and Heathrow Airport, although from early on Tuesday morning there was a shuttle service to Ealing Broadway every 30 minutes.
National Rail has advised:
- Passengers travelling between London and Reading should travel to/from London Waterloo using South Western Railway services
- Passengers in London travelling to Oxford and Banbury should travel from London Marylebone
- Passengers in Windsor traveling to London should travel via Windsor and Eton Riverside to London Waterloo
- Passengers in Windsor travelling west should travel from Windsor and Eton Central to Slough and change at Slough for mainline services to Reading and onwards
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