Analysts believe his departure was a result of the group's continued underperformance over the past 18 months.
Managing director Anthony Skitt will take over Barker's previous responsibilities for group operations and Choices Direct.
Seymour Pierce analyst Rhys Williams said: 'With the underperformance of the group over the last 18 months or so, it is obvious that Steve had not performed to expectations.'
Brokers said the acquisition of a 6.1 per cent stake in the company by Swedish entrepreneur Peter Gyllenhammer could lead to a buyout.
HEC has also reorganised its senior management team, with the appointment of two new members poached from Virgin Megastores.
Doug Morton will be responsible for transforming the Choices UK chain, as director of retail. Joe McNicholas will head the consolidation of purchasing across all HEC divisions.
The latest phase of restructuring will cost about£2million and be completed by June.
HEC recently reported that overall sales decreased by 6.3 per cent to£74,175 in the 28 weeks to December 17.
The operating loss before exceptional costs was£80,000 compared with£3.7 million in 2004. This reflected losses from Choices UK stores.
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