The news comes after a consortium including the fashion chain was named as frontrunner to buy the brands.
Next, which has two outlets in Scarborough, could have been a lifesaver for Dorothy Perkins, Topshop and Topman, which also have stores in the Brunswick Shopping Centre.
In a statement, Next said the consortium had been "unable to meet the price expectations of the vendor".
Some 13,000 jobs were put at risk when Arcadia went bust in November.
This is another blow to the future of the Brunswick Shopping Centre. It comes after last week’s more positive announcement that Debenhams in the town will remain open for now, despite national closures.
Next said it wished "the administrator and future owners [of Arcadia] well in their endeavours to preserve an important part of the UK retail sector".
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