The society said it still intended to proceed with its planned pounds 3bn flotation next year and was hoping to conclude takeover talks with a mutual life insurer before then.
But Mr Stewart admitted that even if an agreement was reached, the full integration of a mutual insurer into Woolwich would probably have to wait until after de-mutualisation takes place next summer. Woolwich is also hoping that other building societies may be willing to talk to it about possible mergers in the near future.
As a further sign that the society is hoping to put the past three months' turmoil behind it, Mr Stewart said he expected an announcement "within days" on the likely compensation package to be paid to Mr Robinson.
The former chief executive's payoff, which will come three months after his ousting for alleged financial irregularities, is thought likely to include either a pounds 165,000 immediate annual pension or a pounds 370,000 tax-free lump sum plus pounds 135,000 a year reduced pension.
Mr Stewart's appointment follows a three-month search for a replacement. Several external candidates, including Andrew Longhurst, chief executive at Cheltenham & Gloucester, are thought to have been interviewed.
Sir Brian Jenkins, chairman at Woolwich, defended the society's use of headhunters to search for a candidate to replace Mr Robinson.
"We felt it imperative to measure the undoubted abilities of our internal candidate against a field measured by an executive search," Sir Brian said.
He added that Mr Stewart had all the right qualities, including "vision, style, energy and integrity", to lead Woolwich into flotation and beyond.
Mr Stewart, who has been with Woolwich since 1977, has in the past 10 years been responsible for the society's diversification programme.
This includes setting up the society's life and general insurance and unit trust subsidiaries, and managing its merger with Town & Country Building Society in 1992.
He denied yesterday that his was purely a caretaker role until the Woolwich was taken over by a potential predator, such as the Prudential.
Mr Stewart said: "We are absolutely bang on target and have not lost a single day because of Peter Robinson's departure. Business could not be going better, as we hope to make clear from our half-year figures next month.
Mr Stewart said that although they had received a number of phone calls from institutions suggesting merger or takeover talks, none had been serious.