It is understood MHP was appointed without a competitive pitch. Brunswick has held the account for seven years.
It follows the appointment of new CEO David Lockwood in December. Lockwood joined from electronic company Laird, which has been an MHP client since 2013. Laird recently took on Centrica's corporate affairs chief.
Last week Cobham reported a sharp fall in annual pre-tax profit, from £280.4m to £175m, as revenue fell from £2bn to £1.9bn.
Chairman Michael Wareing said he was "deeply disappointed" with the "poor outcome". The group cited "weaknesses in management and financial controls", along with "contractual and commercial failures" and "more challenging market conditions" in some areas.
MHP is to advise on the Cobham’s UK financial and corporate communications, reporting to Lockwood and chief financial officer David Mellors, along with the company’s in-house comms and investor relations team.
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