Speaking to the UK's Airports Commission, Matthews claimed that failing to develop Heathrow would lead to both Paris and Frankfurt overtaking it as Europe's leading international hub within a decade.
And he argued that this should not be allowed to happen as London is still in a prime position for global aviation, has strong local demand from a large and global city and is home to "one of the world’s most important network airlines and alliances in the shape of BA and oneworld".
Indeed, with additional capacity, Matthews claimed that Heathrow could provide regular direct connections to 40 more long-haul destinations by 2030, particularly to long-haul emerging market destinations that are important for economic growth.
He added that any move away from the current hub airport model was extremely unlikely, dismissing suggestions that point-to-point and hub models could be integrated, or that low cost carriers could move into long haul markets.
Matthews told the Commission: “These straightened economic times have triggered a global economic race, with both companies and countries competing fiercely.
"If the UK does not want to be left behind by its foreign rivals, it must have the connectivity to compete and trade on the world stage.
"That connectivity can only come from a single hub airport in the right place for taxpayers, passengers and business. Only Heathrow can meet all these demands.”