The purchase of San Francisco-based Pegasus Aviation Finance was expected to complete in "about six weeks" according to a company spokesman.

Terra Firma added that it bought the leasing company from investment funds managed by US company Oaktree Capital Management and Pegasus senior management.

"The purchase of Pegasus builds on our initial AWAS acquisition, and will significantly strengthen our worldwide position within the aircraft leasing sector, by broadening our customer and supplier base," Terra Firma chief executive Guy Hands said in the statement.

"The acquisition will allow the combined company to take advantage of significant benefits from increased scale as well as to capitalise further on the attractive outlook for the sector."

Since 2004, Pegasus Aviation has built a business of 82 owned aircraft, 94 managed aircraft, and a further 37 aircraft on forward orders.

The value of Pegasus-owned fleet, and ordered aircraft, was more than 5.0 billion dollars, according to the statement.

AWAS, meanwhile, leases 134 aircraft to 72 airlines around the world.

Franklin Pray, AWAS chief executive, said: "The combined fleet will comprise more than 250 owned and forward order pipeline aircraft valued at over 7.5 billion dollars and 94 managed aircraft, leased to over 120 customers worldwide.

"Together, we aim to be a major generator of growth in the global aircraft leasing business for Terra Firma."

The private equity sector consists mainly of investment funds or banks that buy stakes in non-listed companies that are then generally broken up and sold for a profit.

Some leading finance officials have warned of the risk associated with private equity groups that borrow huge amounts of money through the company being acquired to help fund the deals. Trade unions, meanwhile, claim that workers face increased risks of redundancy.

Terra Firma was recently beaten by US private equity rival KKR in a takeover battle to win control of British pharmacy giant Alliance Boots.

KKR emerged victorious after bidding 11.0 billion pounds alongside Alliance Boots' executive deputy chairman and key shareholder Stefano Pessina.

Terra Firma's unsuccessful consortium had also included medical charity Wellcome Trust and British bank HBOS.