* Business minister Andrea Leadsom inclined to allow deal
* Decision on deal to come after consultation
* Consultation to run until Dec. 17
* Advent puts forward several legal undertakings (Adds Cobham family comment, updates shares)
By Kate Holton and Noor Zainab Hussain
LONDON, Nov 19 (Reuters) - The British Government has indicated it is likely to allow Advent's $5 billion purchase of defence company Cobham after the U.S. private equity group offered a number of commitments to address national security concerns.
Britain's Business minister Andrea Leadsom had put the deal on hold while she established whether the sale of the air-to-air refuelling equipment maker posed a national security threat.
She said on Tuesday she was now minded to accept the deal after Advent put forward several legal undertakings, including to place a number of British executives on Cobham's boards.
Shares in Cobham were 3.9% higher at 160.8 pence by 0946 GMT.
"We have worked closely with the Ministry of Defence to construct undertakings that would adequately mitigate against any potential national security risks," Shonnel Malani, partner at Advent, said.
Advent will also have to give prior notice to the Ministry of Defence if it plans to sell all or part of Cobham's business, and honour existing contracts with the government.
The government said it would now run a consultation until Dec. 17 on the proposals.
"No decision will be taken on whether to accept the undertakings until the consultation has closed and the representations have been carefully considered," Leadsom said in a statement.
Cobham, which employs 10,000 people and also makes communications equipment for military vehicles, has a storied history but faced difficulties in recent years.
Launched in the 1930s, the company's equipment came to the fore ahead of World War Two and in the 1982 Falklands conflict. Its technology is now used in aircraft such as the F-35 Joint Strike Fighter and Eurofighter Typhoon as well as advanced naval vessels, satellites and military vehicles.
However, the Cobham is still recovering from a string of profit warnings in 2016 and 2017 that forced it to ask shareholders for cash and prompted Chief Executive David Lockwood to overhaul operations.
"This is a significant milestone and an important step towards providing greater certainty for Cobham's employees and customers," Lockwood said in response to Leadsom's comments.
However, Nadine Cobham who holds a 1.5% stake in the company which was founded by her father-in-law Alan Cobham, said the undertakings would "do little" to mitigate risks.
"Countries around the world are raising barriers to protect their own domestic defence industries reflecting rising geopolitical risk ... this government seems content to bargain away our long term security," she said.
Advent is not new to British technology having snapped up electronics company Laird for $1.65 billion last year.
The firm has won approval from regulators in the European Union, U.S. and Finland for its acquisition of Cobham and has been waiting for Britain's nod. Shareholders backed the takeover in September.
(Reporting by Kate Holton in London and Noor Zainab Hussain in Bengaluru; editing by Michael Holden, Kirsten Donovan)