Sorrell and his fellow signatories, including the Conservative Party’s former treasurer Michael Spencer, told David Cameron in the letter that the delays over making a decision were "disastrous" for Britain.
A decision on whether to build a third runway at Heathrow was expected by Christmas but the Government has now delayed it until next year, potentially after next May’s London mayoral elections.
The letter, organised by the campaign group Let Britain Fly, urged Cameron to get a grip on airport expansion and said it was regrettable that he had ducked making a decision.
Signatories pointed to the Airports Commission spending millions of pounds of taxpayers’ money and three years examining evidence – adding that it "was established so that a difficult decision, fundamental to our long-term prosperity, could be made without being bogged down by politics".
Other business leaders to sign the letter include Iain Anderson, executive chairman of Cicero Group and and chairman of the APPC, Martin Gilbert, chief executive of investment firm Aberdeen Asset Management, and Harrods managing director Michael Ward.
Calling for the Government to proceed with Heathrow expansion, they wrote: "The Government should listen to the experts it appointed and just get on with this vital upgrade to our national infrastructure. Every further period of delay is costing the UK economy billions in lost trade and investment and damaging our economic competitiveness.
"The message this sends out to global investors is equally disastrous. We urge the Government to get a grip… by committing to announce a clear and final decision by no later than the end of May 2016."