London Heathrow Airport has released a statement saying that it hopes to “run a full operation tomorrow (Saturday March 22, 2025)”:
“Our teams have worked tirelessly since the incident to ensure a speedy recovery. We’re pleased to say we’re now safely able to begin some flights later today.
“Our first flights will be repatriation flights and relocating aircraft. Please do not travel to the airport unless your airline has advised you to do so.
“We will now work with the airlines on repatriating the passengers who were diverted to other airports in Europe. We hope to run a full operation tomorrow and will provide further information shortly.
“Our priority remains the safety of our passengers and those working at the airport. As the busiest airport in Europe, Heathrow uses as much energy as a small city, therefore getting back to a full and safe operation takes time. We apologise for the inconvenience caused by this incident
Note that the initial priority is to repatriate stranded passengers and aircraft, so a “full operation” certainly does not mean that everything will necessarily be running smoothly.

Bottom line
It’s very good news that Heathrow Airport should be up and running tomorrow. However, the impact of today’s cancellations are likely to spread throughout the weekend (at least), as the airlines get aircraft, crew and stranded passengers back where they need to be.
If you are due to be travelling to/through Heathrow, keep a close eye on updates from your specific airline on social media etc, as well as from the airport itself.