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John Holland Kaye lashed out at the "warm words" from Government and stressed they could not allow a "health pandemic to turn into an economic pandemic".
It comes as Home Secretary Priti Patel prepares to lay out her plans for everyone coming into Britain to quarantine for two weeks from next Monday.
Ministers say it will stop new cases being brought in from abroad and prevent a second wave of the virus.
But travel industry experts say quarantine, which begins on Monday, will cost Britain’s tourism sector as much as £15billion if it goes on through the summer.
But Mr Holland-Kaye told Radio 4's Today programme that passenger numbers would remain low until the Government publish a plan for how to ditch the quarantine.
He said: "We know how quarantine will work, but there has to be an exit plan.
"We have seen warm words, we haven't seen action.
"Unless we can see that, that gives us confidence, we wont be able to take the measures that are needed to get the UK economy moving and to save people’s holidays."
The coronvirus pandemic has been "devastating" for the aviation sector and millions of jobs in tourism and hospitality too.
Businesses are "running out of cash very quickly" and their entire existences are at stake.
He added: "If we don't get a plan from the Government in the next few days on how we are going to reopen the economy, those jobs are at risk.
"As chief executive, I am going to have to make that decision in the next few weeks about jobs in my own company.
"We need to stop this health pandemic becoming an unemployment pandemic."
Minister 'hopes' Brits can go on holiday this year but CAN'T give a date
HOPES for Britain to be able to go on holiday this year were raised today after a minister said it might be possible.
Health Minister Ed Argar said this morning he couldn't give a date of when that might be possible.
He told the BBC: "I would love to be able to give people an answer on that.
"I know the huge toll that this disease and the restrictions are taking on people.
"And I know one of the of the things that many people want to do is have a holiday.
"I am very cautious on this, and I'm not going to say a particular date when that might happen.
"I hope that people will be able to go on holiday at some point this year but I can’t make that promise."
Matt Hancock said last week he is "more optimistic" about getting a break in soon.
And MPs have been voicing their opposition to the plans too , saying the rules are full of loopholes.
Travellers to the UK will allowed to break the two-week coronavirus quarantine to pop out for food, attend funerals and can use public transport, Downing Street said yesterday.
The government confirmed there was a list of exemptions to the controversial rules after a backlash from Tory MPs – but said these were only in case of an emergency.
All arrivals from Monday – except a short list of exemptions – will have to hand over contact details and an address of where they will self-isolate for 14-days.
Public Health England will do random spot checks to make sure people are staying home – and anyone breaking it will be fined £1000.
Those from the Common Travel Area will be exempt, and the measures will be reviewed every three weeks.
Home Secretary Priti Patel said: "Protecting the public’s health and avoiding a second peak that overwhelms the NHS will always be our top priority.
"As we get the virus under control here, we must manage the risk of cases being imported from abroad. We owe it to the thousands who’ve lost their lives not to throw away our progress.
"These measures are informed by science, backed by the public and will keep us all safe."
But today it was reported that the Government didn't seek the backing of its group of SAGE scientific advisers before pushing through with the measures.
Previously ministers have always insisted they will be "guided by the science", yet back in March they did not advise quarantine measures for people coming into the UK.
The Government are also looking at so-called air bridges when it's safe to do so. It would remove the 14-day measures and safely open up routes to other countries with low rates of transmission.
Deals would need to be sealed with each country first.
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