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The owner of British Airways, IAG, has refused to attend a meeting with Home Secretary Priti Patel on Thursday to discuss the UK's new quarantine plans.
From 8 June the government will require all travellers to the UK to quarantine for 14 days or face a £1,000 fine.
However, BA, which is under huge financial strain due to the pandemic, has called it "another blow to our industry".
EasyJet and Virgin Atlantic are among the airlines that have agreed to meet the Home Secretary.
IAG did not give a reason for not attending, however, it's faced heavy criticism in parliament in recent days over a plan to slash jobs while accessing the government's furlough scheme.
In April, BA said it would cut 12,000 roles and weaken terms and conditions for its remaining staff, just weeks after it had put 30,000 workers on the job retention scheme.
The airline has defended the cuts as necessary, however, on Wednesday the aviation minister Kelly Tolhurstwho is attending Thursday's meetingsuggested BA should be held to account for what one MP called a "breach of faith".
"The [furlough] scheme was not designed for taxpayers to fund the wages of employees only for those companies to put the same staff on notice of redundancy during the furlough period," Ms Tolhurst said.
The government insists the new quarantine rules will help contain the spread of coronavirus.
However, the move has been criticised by the UK's tourism industry, which has all however, ground to a halt due to the pandemic.
The boss of the UK's biggest airport services company, Swissport, said on Thursday that the plan could deliver a "killer blow" to the tourism sector.
Michael O'Leary, chief executive of Ryanair, echoed those concerns, saying the requirement to self-isolate would "significantly reduce European visitors".
The manufacturing industry has added to the criticism, warning fewer flights will restrict imports and exports.
On Monday, a group of 200 travel companies wrote to Ms Patel asking for the plans to be scrapped.
The letter suggested travel should be possible for peoplewithout quarantinebetween destinations "deemed safe from coronavirus".
So-called air bridges would allow visitors from countries where coronavirus infection rates are low into the UK, without having to self-isolate for two weeks.
The BBC has contacted the Home Office for a comment.