Their unease follows closely on last week's dispute between GEC and institutional shareholders over a new incentive plan featuring executive performance targets that some regard as insufficiently testing.
The executive, who celebrates his first anniversary at GEC on Tuesday, promised in December to streamline the group patched together over 33 years by his predecessor, Lord Weinstock, and to increase the pace of earnings growth, which has averaged just 4.9 percent in the past decade.
So far, though, Mr Simpson's moves have focused on changing faces in the boardroom and sketching broad plans to focus GEC on its Marconi defence electronics unit, weaning it from joint ventures making rail cars, power generation gear and telephone switches. GEC has yet to announce details of how it will achieve those aims, and shareholders are getting restless.
"There needs to be more done," said Stan Pierson, a fund manager at Scottish Widows Investment Management Ltd, which owns about 1 per cent of the stock. "Whether Simpson is doing enough is up in the air. It's a difficult job to do because it involves a change in mindset of the company, but the jury is still out."
Since Mr Simpson came aboard, GEC shares have lagged behind the the FT- SE 100 index, rising just 2.5 per cent to 391p.
In July, Mr Simpson started a process of "radical change" to enable Marconi to cope with the quick downsizing of military spending at the end of the Cold War. The unit, which makes 30 percent of GEC's pounds 11bn in annual sales, will be the main focus of the group.
His task involves reversing the record of the past decade, a time when GEC sales have doubled but profits have failed to keep pace. This is precisely the reverse experience of the highly successful engineering group Smiths Industries. Smiths' chairman, Sir Roger Hurn, is being touted as a leading contender to come to help Mr Simpson, a boardroom colleagues of many years, by taking on the job of GEC chairman next year.
"We are mindful that GEC is a company that is going through a transition, and we are broadly supportive of the moves that have been made," said Guy Gubb, an investments manager at Standard Life Assurance Co, owner of 2.6 percent of GEC's stock. "But we are keenly interested to see the result."
In private and in off-the-record briefings, company watchers are much more shrill about demanding quicker reform. Even the record of Mr Simpson, hand-picked by Lord Weinstock as a visionary and strategy maker, is questioned. Some say his work at Rover, sold to BMW, and Lucas, merged with Varity, shows that ultimately he's not up to the job of a major remake at GEC.
"He's not been the man to roll up his sleeves and do the actual work of hiring and firing people," said Colin Whitbread, an independent car industry analyst.
Hurn profile, page 6