Planning permission for a Safeway store on the outskirts of Northallerton was quashed by high court judge Mr Justice Dyson last week (see LGCnet). However, he rejected arguments from rival chain Somerfield that new stores needed to improve town centre shopping before they could be allowed.
The judge ruled they had only to show not to be harmful to the town's economy as a whole.
Officials and members of Hambleton DC have decided not to appeal the decision on the grounds it would be expensive and the outcome uncertain.
Local traders who oppose further supermarket developments welcomed the council's decision.