LONDON—The boss of the British Airways owner, IAG, said on Monday its transatlantic bookings had already reached nearly 100 percent of 2019 levels after the United States dropped restrictions earlier this month. Airlines such as BA and Virgin Atlantic had pinned their hopes on the reopening of Europe to United States routes as vital to rebuilding their finances, after more than 18 months of restrictions left them nursing billions of dollars of debt. Luis Gallego told the Airlines UK conference that the group was recovering, and he expected a return to pre-pandemic flying levels by 2023. “Now as the world opens up, we are growing our capacity,” he said. “Transatlantic bookings have already reached almost 100 percent of 2019 levels. I expect North Atlantic routes to reach full capacity by next summer.” Gallego warned however that a move by London’s Heathrow Airport to hike charges could hit the recovery, and …