The group behind a scheme to lengthen one of Heathrow’s runways are reported to have offered to slash the cost by £2 billion in a final effort to win approval from the government.

Heathrow Hub has proposed stretching the northern run­way to 4.2 miles and splitting it in two so that aircraft can take off and land simultaneously. The project could be delivered for £7.5 billion, the privately funded group now says.

It is vying with two other plans to boost airport capacity in south-east England – a third runway at Heathrow and a second runway at Gatwick.

Last weekend Heathrow offered to cut £3 billion from its £16.8 billion plan for a third runway.

The airport’s chairman Lord Deighton suggested it could scrap proposals to divert the M25 through a tunnel beneath the runway, build cheaper terminal buildings and axe a passenger rail system.

Deighton’s eleventh-hour offer reflected repeated criticism from Heathrow’s biggest customer, British Airways.

Willie Walsh, chief executive of BA owner International Airlines Group, has described the scheme as “gold-plated facilities to fleece airlines and their customers”.

Heathrow Hub, conceived by former BA Concorde pilot Jock Lowe and backed by the Marshall Wace hedge fund manager Anthony Clake, hopes to license its scheme to Heathrow for up to £5m a year for 20 years.

It estimates it will have spent up to £10 million on the project, largely on employing consultants. Clake has pledged to hand any profit to charity.

Lowe said the cost-cutting modifications would also entail a more basic terminal and scrapping a rail system, the Sunday Times reported.

He admitted they would “lower the quality” of the Hub project for passengers, but said it would be “simpler, cheaper, quicker and easier” than building a third runway.