Chris Ward, Labour MP for Brighton Kemptown and Peacehaven, hailed the move as a “victory”, having started a petition – Save Wellsbourne Healthcare – which got more than 4,000 signatures.
“I’m so proud of our community for standing up and fighting back against the threat of a private provider replacing Wellsbourne,” he said.
The potential takeover was stopped following a report by the Independent Patient Choice and Procurement Panel found that NHS Sussex had broken procurement rules.
The trust added that it had also taken into account “strong public feedback” in recent weeks.
“Our ambition has always been to ensure that there is the best possible GP services offered to the local residents in this area of the city,” said Amy Galea, chief integration and primary care officer at NHS Sussex.
“We will now… see how best to achieve this,” she added.
Ms Galea said that the GP surgery will continue to run as normal.
The Whitehawk GP surgery, which lies within one of the most deprived areas in Sussex, serves around 8,300 people, according to NHS Sussex.