"Around 85%" of British Airways' schedule at Heathrow will run as planned today, the airline has said in a statement, as it advises passengers to travel to the airport unless told otherwise.

The airline has been the worst affected, travel expert Simon Calder told the BBC earlier.

Its latest statement explains customers will "likely" experience delays however as it offers those booked on flights to or from the airport this weekend "flexible options" to rebook for free.

We're continuing to bring you stories from people who have been impacted by yesterday's disruption at Heathrow Airport.

Jane Davies, a headteacher from County Durham, was stranded in Dubai with eight of her pupils on a school trip.

She says they were just about to leave their hotel when a newsflash came up on her phone about Heathrow being closed.

“My heart sank," she says. "We didn’t say anything to the children, knew we’d just have to get to the airport."

Davies says they later heard the flight would take off, but delayed.

“I’ve got a WhatsApp chat with the parents, just making sure that they’re kept informed all the time because obviously I’m very conscious that they’re sitting at home really worried how their children are coping.”

Image source, Reuters

Heathrow Express has just announced that any unused tickets purchased yesterday will be valid for today.

"Simply see the gateline staff at the barriers, and they will let you through," they say in a statement.

Transport secretary Heidi Alexander also said in a statement earlier that rail tickets can be used flexibly today to help passengers with their journeys.

We've been bringing you stories from people who have been impacted by yesterday's disruption.

Liz was due to attend her youngest son Paddy’s graduation in Stirling, Scotland but was unable to make it.

"It was devastating," she says.

"I know that there are people that have been affected much worse than this, but I’ve been to every other graduation that my kids have had, Masters and undergrads, and I just always thought that I would be there."

A National Grid spokesperson tells the BBC they are "continuing to work closely with the Government, Heathrow and the police to understand the cause of the incident.” 

“Since this unprecedented fire broke out at our North Hyde substation late on Thursday night, our teams have worked tirelessly and in close collaboration with the fire brigade and police to get the situation back under control," the statement adds.

And as we heard from them earlier, they are "deeply sorry" for the disruption caused. They also reiterate that "power supplies have been restored to all customers, including Heathrow, allowing operations to resume at the airport. 

Image source, Reuters

Heathrow Airport says it is fully operational after a power outage shuttered it yesterday. But travellers displaced by the chaos are still working to get home, and the disruptions are expected to continue into the week.

Here's what you need to know this morning:

• Planes have both taken off and landed at the airport today after some flights resumed last night. Arrivals appear to be more disrupted than departures
• A Heathrow spokesperson said the airport would be "fully operational" today - with flights added to the schedule to facilitate the travel of those who have been stranded
• The National Grid has apologised for the disruption caused
• The chief executive of Heathrow Airport, Thomas Woldbye, has told the BBC he is "proud" of the way the airport managed the situation. Speaking to the Today programme he would not comment on questions about if he should remain in his job
• The knock-on effects from yesterday has led to a number of cancellations today - including 80 flights cancelled by British Airways. The airline has also warned travellers to expect delays

BBC Verify's Nick Beake explains in the clip below how Europe's busiest airport was brought to a standstill – and the global impact that followed.

Barry Caffrey
BBC News

There is quite significant disruption at Heathrow Airport today.

British Airways has cancelled 80 flights in total to and from the airport.

Turkish Airlines, Brussels Airlines, Singapore Airlines, WestJet, Air India and Air Canada are also among those to have cancelled flights.

It’s going to be a very difficult day today, not only for cancellation but also for delays.

British Airways is warning passengers for those flights that will go ahead to expect delays.

The advice for passengers is to check with their individual airline ahead of travelling to Heathrow Airport, because it’s a fast-moving and fluid situation.

In addition to this, many planes and crews are in the wrong positions.

There were a number of repositioning flights taking place yesterday evening from places like Gatwick Airport, Glasgow, and Manchester.

But some planes are further afield at places like Shannon Airport, Barcelona, Paris, and in North America.

There is going to be knock-on effect, not only for today but going into tomorrow - and probably into Monday and early next week as well.

Image source, Reuters

We've just seen a statement from airline Virgin Atlantic, who say they are working to ensure passengers can complete their journeys "as quickly as possible".

"Heathrow Airport has fully reopened and we plan to run a near full schedule with limited cancellations today," the statement adds.

The airline adds that Heathrow Airport's closure yesterday has left an "impact on today's flying programme", including the repositioning of aircraft and crews.

A little earlier, our colleagues at Radio 4 asked Heathrow's chief executive if he should remain in his role following yesterday's closure.

Thomas Woldbye said he'd "let others judge" if he should leave his post. You can watch the full exchange in the clip below.

The first planes have landed at Heathrow this morning after a day of disruption yesterday.

Here are some of the scenes from the airport. We can see big smiles from some travellers and hugs at the arrivals gate - and some planes taking off and landing after yesterday's disruptions.

Image source, Reuters

Image source, Reuters

Image source, Reuters

Image source, Reuters

Woldbye is asked how long it will take to get stranded passengers to their destinations.

He says that question is for the airlines to answer and will vary based on where people are in the world and which airlines are involved.

With that, the interview concludes.

Presenter Emma Barnett now asks Woldbye whether he should still be in his role.

"No comments to that," Woldbye replies.

"What do you mean no comments to that?" Barnett pushes back.

"I'll let others judge that if they think it is an issue," Woldbye responds.

"When we know more about the information and what caused it and how it was handled?" she asks.

"Yes," he says.

Woldbye is asked about comments from the owner of freight company PS Forwarding, who said earlier that the UK has become "a laughing stock" following yesterday's events.

He says these comments were made without insight into how big the incident was and that he is "proud" of what people did to get the airport out of the situation.

Barnett pushes him on his comment that he is "proud" of the response to the outage - Woldbye defends this and says the same would happen at other airports.

Woldbye is asked by Emma Barnett on the Today programme why such critical infrastructure appeared to depend on a single power source without an alternative.

He explains there is not a "single source" powering the airport, but three substations that Heathrow works with that power different areas.

Woldbye adds that the situation yesterday was "unprecedented" and considered a "major incident". He says that the airport shut for hours and "not for days" while they tried to re-route the power supply.

Woldbye says he is "sincerely sorry" for inconvenience to passengers but defends the airport's handling of yesterday's closure, saying that the power substation is not part of Heathrow's infrastructure.

"We were handling the consequences of that failure," he says.

Woldbye says their backup systems were up and running yesterday, but they are not designed to power the entire airport.

"Heathrow uses as much energy as a city every day," he says adding that airport infrastructure comes to a standstill when an event like this happens.

Chief executive of Heathrow Airport, Thomas Woldbye, has just started speaking with the Today programme.

Asked how many flights will be delayed or cancelled today, he insists they don't expect "major amounts" but says there will be delays and cancellations on any "busy day".

He underlines the airport is operating "as normal" but says airlines will have to deal with passengers who are stranded as a result of yesterday's disruption.

We're about to hear from Heathrow Chief Executive Thomas Woldbye, who will shortly be speaking to Radio 4's Today programme.

You'll be able to follow along by clicking Watch live at the top of the page - but we'll also be bringing you the main lines right here, so stay tuned.

Lynette Gracias was due to start her 10-day holiday to Dubai yesterday before her flight was cancelled.

She managed to book onto a flight today which has also since been cancelled. Lynette is now hoping for a flight later on tonight.

She spoke with our colleagues at Radio 5 Live a little earlier and criticised the communication she received from her airline.

Lynette says she leant on news outlets for details about the cancellations as they were "more informative that anything else".

She adds that the live chat system for the airline was too busy to respond to her queries, as was the telephone number that they sent out via email.

"It was just wait and see and hope for the best."

Image source, PA Media

The National Grid has said it is "deeply sorry" for the disruption caused by yesterday's power outage.

The electricity supplier says in a statement issued shortly after 06:00 GMT that power has been restored to all customers connected to their North Hyde substation, including Heathrow.

"We are now implementing measures to help further improve the resilience levels of our network," the statement continues.

"We are deeply sorry for the disruption caused and are continuing to work closely with the Government, Heathrow and the police to understand the cause of the incident."