It was listed on the London Stock Exchange until it was acquired by Cascade Investment, Blackstone Group, and private equity firm Global Infrastructure Partners in May 2021.

[4] Its early name came from its two founders, Sir William Fenton and Walter Cobbett, who established the company during 1879 to manufacture textile belts for use on industrial machinery.

[5] For its first thirty years, the production and sale of these belts comprised the company's main commercial activity; over time, Wilson Cobbett expanded into numerous specialist industrial niches and developed a global presence.

[5] During 1992, the company was involved in the creation of Signature Flight Support through the merger of Page Avjet, an executive aircraft interiors business, and Butler fixed base operations.

[13] During 2002, the group's chief executive Roy McGlone stated that management's strategy at that point was to focus on its FBO ventures and to dispose of non-core businesses.

[22] That same year, BBA Aviation reportedly withdrew from talks with Dubai Aerospace Enterprise over acquiring aircraft maintenance provider StandardAero.

[30] During late 2019, BBA Group decided to sell Ontic to CVC Capital Partners in exchange for $1.365 billion; the firm also announced a special dividend to shareholders totalling $835 million from the proceeds of the sale.

To reflect its change in business focus, the company's board also elected to rename the group Signature Aviation to better align the firm with its most significant brand in its core market.

[31][32] In February 2021, Bill Gates–owned Cascade Investment, Blackstone Group, and private equity firm Global Infrastructure Partners made a $4.7 billion offer to acquire Signature Aviation.