Dr Simon Worrell, global medical director of Collinson, told the BBC: "As soon as we can drop it, we will be delighted."
Currently, all those aged five and over arriving in England must take a supervised lateral flow test test within 48 hours of their arrival.
Earlier this week, prime minister Boris Johnson said the government was reviewing its testing rules and that an update from the health secretary would follow "in the coming days".
Worrell said airport testing was "only ever supposed to be a Band-Aid, a temporary solution to get trade and tourism staggering while we build up immunity and we are able to fight the virus by ourselves".
"We are at that point now," he added. "The link between getting infected and hospitalisation has been broken. We are in a fantastic place – the envy of the world, I think."
