Global Infrastructure Partners has agreed to buy private jet services company Signature Aviation for £3.4bn, outbidding buyout group Blackstone and Bill Gates’ wealth manager Cascade Investment.

Signature on Monday said it had reached an agreement on a $5.50 (£4.05) per share offer from GIP, valuing the FTSE 250 listed company at about $4.6bn.

However, the battle for control of the group is still live as Signature welcomed higher offers from rivals, including Blackstone and Cascade as well as private equity group Carlyle, which has disclosed an interest.

“For the avoidance of doubt, nothing precludes either Blackstone and Cascade or Carlyle from making an offer proposal that the board of Signature Aviation will consider,” the company said on Monday.

The GIP offer, a 51 per cent premium to Signature’s share price before the takeover battle began, came days after Blackstone teamed up with Signature’s largest shareholder Cascade, which manages Mr Gates’ fortune, for a possible bid at $5.17 per share.

The Signature board, led by industrialist Nigel Rudd, said in December it was minded to accept a bid at that price, having rejected an earlier lower offer from GIP. Signature also disclosed interest from Carlyle.

Mr Gates’ Cascade owns 19 per cent of Signature, and has committed not to work with any other company on a takeover if Blackstone makes a formal offer, which it has not yet done.

Cascade has also said that, if it and Blackstone were to make a firm offer, it would vote against any competing proposal.

Such an offer would set the stage for a prolonged battle. GIP’s bid needs the support of 75 per cent of Signature shareholders, meaning that Cascade’s 19 per cent stake would be a significant hurdle even if GIP raised its bid above any fresh offer from Blackstone and Cascade.

Signature, formerly known as BBA Aviation, does not own or operate any aircraft. Instead, it offers its suitors exposure to the growing private jet market in America via its sprawling network of refuelling and maintenance bases scattered across the country.

The private jet market has not been immune to the disruption caused by Covid-19, but many operators have recovered more quickly than their commercial rivals.

GIP, the owner of Edinburgh airport, said it was attracted by Signature’s scale and existing customer relationships, and saw an opportunity to add further acquisitions.

“The resilient performance and strong financial position through the pandemic has enabled the Signature directors to consider its future and evaluate this offer from a position of strength,” Mr Rudd said.

Adebayo Ogunlesi, chairman and managing Partner of GIP, said he expected market conditions and earnings to “remain subdued for some time”.

But he said the private equity company’s experience in long-term infrastructure investments made it the “ideal partner” for Signature.