Morley, which is owned by insurance firm CGNU, has increased its stake from 8.95% to 10.07%. The increase was announced in a statement to the London Stock Exchange this morning.
The news edged Aegis shares up slightly to 103.5p from last night's close of 102.7p.
The company's shares have suffered in recent months. They have fallen steadily from a high last September of 205p to today's price.
Aegis is one of the few independent advertising and media firms left and it is viewed as a likely takeover target. Speculation was renewed last week when the French group Havas Advertising made an agreed £425m bid for Tempus Group, the smaller Aegis rival which owns the CIA media buying group.
The outcome of that deal is still undecided as the industry watches and waits to see what WPP CEO Sir Martin Sorrell will do. WPP is Tempus's largest shareholder, owning 22% of the company.
Earlier this year, WPP was pursuing a share-swap deal that would see it swap its stake in media-buying group Tempus for a stake in Aegis.
Such a deal would have seen WPP swap its stake in Tempus for a 5% stake in Aegis, which is valued at £1.3bn compared with Tempus's £332m.
However, Aegis CEO Doug Flynn is believed to want to pursue an independent path for the company. In an interview with the Wall Street Journal, he said, "We believe we can grow the company quicker than any of the big conglomerates can. In terms of scale, we have been winning business and competing comfortably."
In June, Philips Electronics awarded Carat its $600m (£428.1m) consolidated global media account following a three-way pitch and a four-month review.