Cobham, the UK aerospace and defence supplier founded by a British aviation pioneer, has agreed to be bought by a US private equity firm in a £4bn deal that could test the new government’s tolerance of foreign takeovers.

Advent International has agreed to pay Cobham’s shareholders 165p in cash for each of their shares – 34% more than the company’s closing share price on Wednesday. The FTSE 250 company’s board will unanimously recommend the takeover to shareholders.

The shares rose 35% to 166p on Thursday after the takeover was announced.

Cobham employs about 10,000 people, including 2,000 in the UK, and operates in more than 100 countries. The company supplies radar and other electronic products for the defence and aviation industries including world-leading systems that allow planes to refuel in mid-air.

The company was founded as Flight Refuelling Ltd in 1934 by Sir Alan Cobham, a pilot in the first world war who became a trailblazer of long-distance flying. Cobham’s technology made air refuelling widespread and gave RAF planes the range they needed to carry out missions in the Falklands war of 1982.

Cobham has only recently stabilised itself after five profit warnings between 2015 and 2017. It raised £500m from shareholders in 2017 to strengthen its finances after taking on too much debt for the botched takeover of Aeroflex in the US.

The acquisition of a British defence contractor by a US buyout group could face political resistance. Melrose Industries’ hostile takeover last year of GKN, another engineering company that supplies the defence industry, was opposed by unions and some MPs.

The former business secretary Greg Clark sought binding assurances from Melrose about its commitment to the UK. The government has also toughened up rules on foreign takeovers, particularly on national security grounds.

With new cabinet ministers only appointed this week it remains to be seen whether the Cobham deal will be viewed as the buying up of a valuable UK asset or welcome foreign investment. The companies were briefing ministers and parliamentary committee chairs on Wednesday to gain their support.

John Colley, professor of practice at Warwick Business School, said: “This will serve as a first test for the government when we will find out how protectionist they will be. At present the new government is such an unknown that it is almost impossible to know how they will jump. However they certainly have the powers to stop the deal now as a matter of defence security.”

Cobham said the takeover would give shareholders the opportunity to cash in their shares and that Advent would invest in the business to help it grow. The offer is 50% higher than Cobham’s average share price over the past three months but at Wednesday’s closing price of 123p the shares had halved since peaking in 2015.

David Lockwood, Cobham’s chief executive, said: “We have worked intensively over the last two and half years to focus on our customers and our financial and operating performance.

“This offer reflects the potential for future growth and improving performance, and is an endorsement of our turnaround strategy and our hard working people.”

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Advent’s recent deals in the UK include buying Laird, an electronic components maker, for £1bn last year. Lockwood was Laird’s chief executive before he took over at Cobham in December 2016.

Cobham published its first-half results alongside the takeover announcement. In the six months to the end of June underlying operating profit, excluding proceeds from asset sales a year earlier, rose 12% to £107.1m.

The deal will require approval by at least 75% of shareholders at a meeting held no later than October. Cobham’s directors, who own 0.04% of Cobham between them, and Artemis Investment Management, which owns 5.13% of Cobham shares, have agreed to vote for the deal.

Private equity firms are awash with funds for deals and are scouring markets for companies to buy. Until recently deal activity in the UK had dwindled because of concerns over Brexit.