LONDON, July 26 (Reuters) - London"s Heathrow Airport and Britain"s main airlines urged the UK to open up travel to vaccinated passengers or face more job losses, as hopes rose that travellers from the United States could be given the green light this week. Heathrow Chief Executive John Holland-Kaye said Britain could exempt fully vaccinated U.S. citizens from quarantine in the coming days, in what would be a huge boost to the country"s aviation industry which continues to be plagued by uncertainty. Strict rules which the government has previously altered with little notice has meant that Britain"s travel sector remains in the doldrums while Europe"s has partially recovered. Airlines UK, the industry body representing British Airways (ICAG.L), Virgin Atlantic, easyJet (EZJ.L) and others, warned more aviation jobs would go if the government did not make changes at its next travel review expected later this week. It wants quarantine to be scrapped for fully vaccinated travellers from the United States and the European Union, with more countries added to Britain"s green list for low risk travel. Holland-Kaye noted the EU had opened up unilaterally with the United States, adding: "There"s no reason why the UK shouldn"t do the same. I think that could happen this week." Heathrow, which before the pandemic was Europe"s busiest airport, said Britain"s travel restrictions were suppressing trade volumes and traveller demand, pushing its cumulative pandemic losses to $4 billion. A passenger walks with her luggage at the Terminal 5 departures area at Heathrow Airport in London, Britain, May 17, 2021. REUTERS/John Sibley A passenger walks with her luggage at the Terminal 5 departures area at Heathrow Airport in London, Britain, May 17, 2021. REUTERS/John Sibley Passenger levels at Heathrow were about 20-25% of their pre-pandemic levels, while European airports are already back to about 50%, said Holland-Kaye. "Without the passenger planes going to global markets like the U.S., UK exports aren"t getting out of the country, and the UK will fall behind and that will cost jobs, unless we open up," he told Reuters on Monday. For the whole of 2021, Heathrow forecast 21.5 million passengers would travel through its terminals, a big jump from 4 million in the first six months of the year as travel returns, but a long way off the 81 million who used its facilities in 2019. Holland-Kaye said he was encouraged by a recent pickup as school holidays started. Separately Ryanair (RYA.I) said it was seeing strong summer bookings. Heathrow said worries over potential new UK restrictions or other countries barring UK travellers, had pushed it to seek a waiver of its Heathrow Finance ICR covenant for 2021 to cover it in case passenger numbers significantly miss its 21 million forecast. For the six months to June 30, Heathrow posted an adjusted pretax loss of 787 million pounds, compared with a 471 million loss for the same period last year. ($1 = 0.7274 pounds)