According to The BBC, the Luton Topshop and Topman stores in The Mall at The Arndale Centre and the stores in the Harpur Centre, on Midland Road, Bedford will shut as part of a 23 store closure plan, putting 520 jobs under threat.
Under the proposal, Burton, Dorothy Perkins and Topshop stores will close and rents will be cut at another 194 stores at the Arcadia group.
The proposal states that Arcadia Group is prepared to put an additional £100m into the scheme over a number of years to bridge a shortfall in pension contributions, but the regulator does not think the plans are sufficient.
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Ian Grabiner, chief executive of Arcadia Group, called the steps "tough but necessary" to mend the business.
A total of 200 of its UK stores have shut over the past three years.
The BBC claim this is a seen as a final effort by a company to stave off administration or breakup.
Full list of store closures
Aberdeen Dorothy Perkins, Burton
Ashton under Lyne Topshop, Topman
Bedford Topshop, Topman
Bluewater Miss Selfridge
Cork Dorothy Perkins, Evans
Dublin Evans, Wallis
Dublin Topshop, Miss Selfridge
Dublin Topshop, Topman
Fareham Topshop, Topman
Galway Miss Selfridge
Glasgow Burton, Topman
Luton Topshop, Topman
Newcastle upon Tyne Outfit
Nuneaton Topshop, Topman
Reading Dorothy Perkins, Burton
Salisbury Topshop, Topman
Southend Miss Selfridge
Stirling Dorothy Perkins, Burton
Swindon Dorothy Perkins, Burton
Swindon Miss Selfridge, Wallis, Evans
York Dorothy Perkins, Burton