Although the Moores family which owns the embattled Littlewoods empire ruled out any outside bids last Thursday, Mr Walker fears he has shown his hand to investors - and they might not like what they see.
Mr Walker admits that the approach to Littlewoods - part of a pounds 1.1bn consortium bid with mail-order group N Brown - was opportunistic in the extreme. "It wasn't part of any strategic grand plan. If you are out jogging and you trip over a golden nugget you don't just carry on running. You stop and pick it up." But he denies that an interest in Littlewoods' clothes to interior furnishings stores, where Iceland has no management expertise, shows a lack of confidence in the existing strategy.
Instead, he points to Iceland's "outstanding track record", noting that of the 3,000 or so companies listed on the stock market, Iceland is one of only 13 to show earnings per share growth in each of the past 10 years. "And we've been doing it for the past 25 years. Our track record is outstanding."
He also insists that Iceland's acquisition record is good, having successfully integrated Bejam, a frozen-food retailer two-and-a-half times Iceland's size that was bought in the late 1980s.
Some investors prefer a different version of events. They recall the ill-fated foray into French frozen food retailing via the pounds 4m acquisition of Au Gel and the ill-timed switch of emphasis away from frozen to chilled food, just as severe price competition between the superstores and the discounters broke out two years ago.
But their biggest concern is that Iceland operates in a fiercely competitive and mature food retailing market. From a peak of almost 250p two years ago, the shares have been dull performers. Like-for-like sales fell by 3.5 per cent in cash terms in July and August, though Mr Walker says they are now positive again.
The problem from an investment angle is that Iceland seems caught between a rock and a hard place. If it sticks to its knitting in frozen food and rolls out 50 or so stores a year on top of the existing 750, it will struggle to achieve the double-digit earnings growth to which the City has become accustomed.
"The prospect of slowing profits growth is not one to get the City very excited about the shares," says one analyst. "An extra strand of potential growth is needed."
A progressive dividend policy and a share buy-back scheme would help to keep fund managers happy - despite its heavy capital expenditure programme, Iceland throws off pots of cash.
But the City is rather bored with companies that have nothing better to do with the surplus money they generate than to give it back to shareholders. As another analyst puts it: "You might as well invest in gilts in that case."
The alternative is for Iceland to embark on an expansion strategy into non-frozen food or overseas activities, but that would increase the risk profile. The Littlewoods approach was certainly no leap in the dark, as Iceland has operated food halls in 38 branches of Littlewoods since 1992. Indeed, Mr Walker reveals that the first feelers were put out to Littlewoods back in January, long before rival bidder Barry Dale, the former Littlewoods chief executive, made his move.
However, Mr Walker insists that there are no other plans to diversify, even if the feeling persists that he may not be able to resist acting on impulse again if another opportunity such as Littlewoods arises. In the meantime, he is concentrating on expanding Iceland in Ireland - north and south of the border.
An olive branch is still being held out to the feuding Littlewoods board members, but Iceland's plans to become what one analyst called "an affordable Marks and Spencer" are very much back in cold storage.
That leaves Mr Walker to contemplate the equally frosty reception Iceland has received in the City this year - the shares currently stand on a substantial discount to the food retailing sector.
If Mr Walker continues to feel his message is not getting across, and the shares fail to defrost, he may have only one exit route. He could always try an emulate other "misunderstood" companies such as Virgin, Amstrad and the Body Shop and try to take Iceland back into private hands. But that is speculation and little reason to hold the shares.
Share price 154p
1993 1994 1995* 1996*
Sales pounds 1.18bn pounds 1.3bn pounds 1.36bn pounds 1.47bn Pre-tax profits pounds 65m pounds 70m pounds 72m pounds 76m Earnings per share 15.5p 16.7p 15.3p 15.9p Dividend per share 3.8p 4.2p 5.3p 6.5p Price-earnings ratio - 9 10 10 Gross yield - 3.4% 4.3% 5.3%
* SBC Warburg estimates