Sir Martin Sorrell’s iron grip as chief executive of WPP is under threat after the advertising group hired a law firm to investigate an allegation of personal misconduct.

Sorrell, 73, “unreservedly” denies the allegation, which is thought to involve improper use of company funds.

The investigation will put pressure on Sorrell, who is one of Britain’s best-known – and most highly paid – business leaders.

He founded the company as a two-man operation in a London office in 1985 and under his three-decade tenure running the business it has grown into the world’s largest marketing services group with about 134,000 staff in more than 100 countries.

“The board of WPP has appointed independent counsel to conduct an investigation in response to an allegation of personal misconduct against Sir Martin Sorrell, chief executive officer of WPP,” the company said.

“The investigation is ongoing. The allegations do not involve amounts which are material to WPP.”

Sorrell said he rejected the allegation but understood that the company had to investigate the matter. “WPP is investigating an allegation of financial impropriety by me, specifically as to the use of company funds,” he said.

“This allegation is being investigated by a law firm. I reject the allegation unreservedly but recognize that the company has to investigate it. I understand that this process will be completed shortly. Obviously, I shall play no part in the management of the investigation under way.”

The question of who will eventually succeed Sorrell is raised annually at the company’s annual shareholder meeting. WPP has always maintained that there is a list of potential internal and external candidates that is monitored and refreshed, however Sorrell has never given any indication that he may be ready to step back.

WPP shares have come under pressure recently – last month the company said the past year was its worst in growth terms since the 2009 advertising recession. They fell 2% in early trading on Wednesday in response to the investigation.

Sorrell said 2017 “was not a pretty year” for the company but denied it was because his agencies were being cut out of deals between advertisers and Google and Facebook.

Sorrell, one of the UK’s highest-paid chief executives, who has taken home well over £200m in the last five years, said WPP spent more than $6bn (£4.4bn) of its clients’ advertising and marketing money with Google, its biggest single investment, last year, a 10% rise. Facebook received about $2.1bn of its ad spend last year, a 30% rise.