The airport said ministers should "reassess" testing requirements for fully vaccinated travellers and the role of passenger locator forms.
It wants the government to reconvene its Global Travel Taskforce to review the current regime and look at how it can "ensure the UK is aligned with its European competitors".
Heathrow’s plea came as it posted its latest traffic figures on Thursday (11 November), which saw the airport report a sixth consecutive month of growth after more than three million passengers travelled through Heathrow.
"Relaxation of travel rules ahead of half-term unleashed pent up demand, with close to 100,000 travellers a day – up 144% compared with the same time last year," said the airport.
However, Heathrow said "despite signs of recovery", passenger numbers were still down 56% compared with pre-pandemic levels, and warned the UK risked being left behind.
"With air travel at other major European airports recovering faster, ministers should reassess testing requirements for fully vaccinated passengers and the passenger locator form at the next Global Travel Taskforce review to ensure the UK is aligned with its European competitors," it said.
Heathrow has also urged the government to introduce a "price stability mechanism" to encourage investment in the production of sustainable aviation fuel (SAF) and also to mandate a 10% SAF blend by 2030, rising to "at least" 50% by 2050.
"As the recovery continues, our focus remains on the race to net zero," said Heathrow. "Sustainable aviation fuels hold the key to cutting carbon today. British Airways demonstrated the capabilities of SAF earlier this week, powering their first flight back to the US with 35% SAF – the highest level for a commercial transatlantic flight ever used."
John Holland-Kaye, Heathrow chief executive, added: “As the journey to recovery accelerates, aviation’s ambitions to decarbonise must keep pace. We need to keep our foot to the pedal, working to make air travel guilt-free and government must act with a mandate for 10% SAF by 2030 and a price stability mechanism to upscale SAF usage if we are to tackle the industry’s biggest challenge - carbon.”
Heathrow also touched on the current CAA consultation on the passenger fees the airport can charge, with Heathrow seeking to almost double them from £19.36 to £37.63, ostensibly to make up some some of the losses it suffered during the pandemic.
The CAA, though, will introduce an interim price control of £30 per passenger in January. It is currently consulting on a permanent fee threshold, which will fall between £24.50 and £34.40 per passenger.
Heathrow said the CAA settlement should "reflect the size of the asset and costs required to run and invest in it".