Commenting about GKN's intention to separate the businesses, Melrose said it believes that shareholder value would be maximised by it significantly improving the businesses prior to any separation.
GKN, which used to be known as Guest, Keen and Nettlefolds and traces its history back to 1759, has struggled in recent years and its profit warning came after a downturn in its U.S. aerospace business.
By 11.20am, GKN shares had extended their earlier gains to over 26%, up 87.3p at 420p, while Melrose shares gained 5.4% or 11.6p at 226.6p.
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The automotive and aerospace parts manufacturer confirmed in an update on Friday that it had received a "preliminary and unsolicited proposal from Melrose" on 8 January worth 405p per share, a 24% premium to its closing price on 5 January of 326p.
The engineering group also announced the appointment of interim boss Anne Stevens as the group's permanent chief executive.
In November, the company announced that its CEO designate Kevin Cummings was leaving the company with immediate effect following a profit warning brought about by difficulties on United States aerospace operations.
GKN's board dismissed the offer from Melrose in a unanimous decision. The offer would have resulted GKN shareholders owning 57% of the combined company and and Melrose shareholders holding 43%.
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Ms Stevens, who at 69 has extensive experience in the aerospace and automotive sectors, said she would instill a much stronger performance and accountability culture at the group, which employs 58,000 people across 30 countries. "I am relishing the challenge of delivering that potential with a new group-wide improvement programme underway".
At the same time, having undertaken an intensive analysis of the economic benefits and costs involved, GKN said it intends to separate its automotive and aerospace businesses, saying the move recognises "the strategic optionality for shareholders in having separate companies with distinct investment profiles and capital allocation policies".
It said: "The board will communicate further details on the optimal method of separation in due course".
Market sources suggested companies such as Spirit AeroSystems or Triumph Group could be suitors for GKN's aerospace business.
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Involving paper in its GKN bid is a departure from its usual strategy of raising funds for acquisition through rights issues. It carried net debt of around £700 million as of June 30th, 2017.