Cubitt director Michael Henman is advising Robinson's buy-out vehicle Raphoe Management, which said on 22 August that it would approach Rentokil's board about an offer for the company.
Raphoe could make a cash and shares offer for Rentokil, a deal that would leave shareholders with more than 90 per cent of the firm.
Robinson, who built his public profile as a troubleshooter on the BBC series I'll Show Them Who's Boss, would replace the firm's executive chairman Brian McGowan and oust its recently appointed chief executive Doug Flynn.
McGowan's takeover of Rentokil led to the appointment of Brunswick as the firm's retained adviser (PRWeek, 28 May 2004).
Last Friday, Rentokil revealed a 40 per cent slide in pre-tax profits.
The firm insisted it would not break itself up to fend off predators.