In a letter written to health secretary Sajid Javid, they argued the restrictions should be removed for fully vaccinated travellers "at the very least".
They also claimed international travel was one of the few areas where "there is no return to normal yet".
The letter was signed by Tui managing director Andrew Flintham, Ryanair boss Eddie Wilson, easyJet chief Johan Lundgren, Loganair chief executive Jonathan Hinkles, British Airways chief Sean Doyle, chief executive of Virgin Atlantic Shai Weiss, Jet2.com boss Steve Heapy and Airlines UK chief Tim Alderslade.
In the letter, the bosses put forward "three key demands to finally return air travel to near normality".
They included restriction-free travel, the implementation of "a clear protocol" for managing future variants and the ruling out of border closures and flight bans in response to future variants of concern.
"These measures would send the strongest possible signal that the UK has turned a corner, is truly looking to live alongside the virus, and is mobilising its world-beating aviation sector to turbo-boost our recovery and deliver global Britain," the letter read.
"Last summer saw restriction-free travel across Europe for the fully vaccinated, with no signs this led to worse outcomes than the UK experienced.
"A number of countries are already moving back to this position, including Germany, Spain and Switzerland, who now require no testing for the fully vaccinated.
"It is time for passengers and businesses who rely upon the UK’s air connectivity to fully benefit from the same vaccine dividend that has enabled our domestic economy to reopen."
It also pointed to recent research from Edge Health and Oxera, which demonstrated the "limited effect" of travel restrictions in reducing the spread of the Omicron variant.
