British Airways is said to have demanded £10million from Heathrow after the luggage fiasco over the weekend which saw 20,000 bags fail to make it onto flights.The airline's chief executive, Sean Doyle, reportedly wrote to his counterpart at the airport, Thomas Woldbye, to request compensation after the luggage systems at Terminal 5, BA's main hub, broke down on Friday.He also asked Mr Woldbye for assurances that there will not be a repeat of the system failures in the terminal and for contingency plans to be drawn up.The technical fault saw arriving passengers stood around waiting for their bags or going home without them and departing passengers later found out their bags had not been loaded on to the plane.It was the fifth time there have been issues with the baggage system since the start of the year and this one incident cost BA £10million and a blow to their reputation.In the February half-term holiday, a similar incident affected 7,000 bags and another at Easter affected 4,000.Pictures of the travel chaos on Friday emerged online showing droves of luggage and essentials abandoned across the terminal. It is understood Heathrow Airport is responsible for outbound baggage, while individual airlines hold responsibility for inbound luggage. Baggage chaos erupted in Heathrow airport on Friday as hundreds of bags transported by British Airways were abandoned in Terminal 5 Pictures of the travel chaos emerged online showing droves of luggage abandoned across the terminalInbound luggage does not enter an airport's system and is taken from a flight by an airline's ground handler and brought to the reclaim halls for passengers to collect.On Friday, BA apologised to passengers but said the issues with the system were out of its control. It has deployed extra staff to resolve the remaining baggage issues as quickly as possible.A BA source told The Times that the company 'can't keep absorbing the consequences of repeated Heathrow system failures'.They said the five incidents that have occurred so far this year 'highlight a clear need for more resilient infrastructure and stronger contingency planning at the airport'.The source also said BA customers 'rightly' expect and pay for a 'reliable journey', adding that it is those customers who 'suffer when these appalling failures happen'. 'As decisions are made about the airport's future, it's essential that reliability and resilience come first,' they added.A Heathrow spokesperson said: 'We are really sorry for the inconvenience and frustration caused by the baggage incident last Friday. 'The system’s reliability is fully restored, and we have been working closely with BA to reunite bags with their owners. Our baggage system operates with 99 per cent reliability despite Heathrow operating at full capacity. 'We will continue working with airlines and their ground handlers to minimise future incidents and drive opportunities to make baggage performance even more reliable. 'We hope the CAA will see the value these improvements will deliver for our customers and support future investment.'After the issues on Friday, one passenger aired their fury on X, writing: 'British Airways really disappointing with arriving back to T5 and total chaos at baggage arrivals.'Families waiting hours and told to go home as baggage abandoned all over airport.'Another branded the situation an 'absolute joke', writing: 'Flight landed at 10:35 was delayed from getting of the plane for 30 minutes.'To then arrive at baggage reclaim waited 3 hours and two belt changes to be then told all the staff have gone home and you can't get your baggage.' Luggage chaos also ensued for those travelling out of Heathrow amid technical issues which saw some flights leave without baggage onboard It is understood Heathrow Airport is responsible for outbound baggage, while individual airlines hold responsibility for inbound luggage'What a shambles,' a passenger penned. 'No communication, no luggage and now your website is down to report the non retrievable luggage.'What is a customer supposed to do. Flight from Larnaca into Heathrow last night. Advise what I'm supposed to do?'A customer branded the service from British Airways as 'awful' and 'totally unacceptable' as they asked when they would be receiving their essentials.Others claimed passengers were instructed to leave the airport without their luggage and told to file a lost baggage report.Meanwhile, baggage chaos also ensued for those travelling out of Heathrow amid a technical issue which saw some flights leave without baggage onboard.A traveller claimed to have seen their luggage 'sitting on the ramp beside' their aircraft in terminal five, while the plane departed 'without it being loaded'.They added: 'We informed cabin crew but nothing was done. Traveling with seven checked bags and an infant.'A mother voiced her fury that her daughter's 21st birthday celebrations in Dublin had been ruined by the fiasco.'British Airways my daughter flew from Heathrow yesterday to Dublin arrived to find no cases and been out on the flight,' she said.'No idea when they will receive them or if they even will. There for her birthday weekend for 21st birthday and absolutely ruined.'A newlywed told how she was left 'devastated' to discover her bags were lost after landing in Corfu.'On our honeymoon in Corfu and British Airways have lost our bags,' Daisy wrote.'Absolutely devastated, never had this issue in 15 years and it happens on our honeymoon. Poor communication hours of waiting around and no bags arrived.'Daily Mail has contacted British Airways for comment.