Danson, who was unavailable for comment, paid around £275,000 last week for 935,909 shares, taking his holding from 24.01% to 25.28%. TMN shares are currently trading at 29.5p after moving between 28.5p and 30.5p last week.
Owning 25% of the company allows Danson to block the passing of special resolutions, which would be required to delist it, thus limiting the ability of others to make bids.
He was not involved in a recent £52.8m, 70p per share bid for TMN put together by its chief executive Mark Smith, chief financial officer Craig Dixon and private equity firm August Equity.
The bid collapsed in July when August Equity admitted it was unable to secure funding.
TMN Group companies include full service digital advertising agency EDR, online market research arm ID Factor, and research analysis agency ICD Research.
Danson first emerged on the shareholder register around the time TMN received a 50p per share offer from Tangent Communications in March, which was subsequently withdrawn.
In 1990 he started Datamonitor, which was sold to Informa in 2007 for £502m. According to the Daily Telegraph, Danson made a total of £165m from the business.
In April this year he bought a 50% share in left-wing weekly magazine New Statesman from Labour MP Geoffrey Robinson, who retained 50%.