Sky News has learnt that the FTSE 100 supermarket chain is working with headhunters to identify Mr Allan's successor.

City sources said a number of heavyweight boardroom figures had been approached in recent weeks about the role.

Mr Allan will step down next year, by which time he will have served for nearly a decade and be 'timed out' under corporate governance guidelines which mean that he would no longer be regarded as independent.

The search for his successor is being led internally by Byron Grote, the former BP finance chief, who himself is due to step down from the Tesco board this year.

Lygon Group, a search firm, has done much of Tesco's boardroom recruitment work in recent years, although Tesco declined to confirm that it was overseeing the chairman process.

Mr Allan, a former president of the CBI, has been an outspoken figure during his tenure as Tesco chairman, and has been lavishing praise on the Labour Party leadership in recent months.

A former chairman of Dixons Stores Group - now known as Currys - he has also sat on the boards of blue-chip British companies including 3i Group, Royal Mail and Worldpay.

Barratt Developments, the FTSE 100 housebuilder also chaired by Mr Allan, recently completed the search for his successor.

He was appointed as chairman of Tesco during the aftermath of the biggest crisis in the chain's history, with the discovery of an accounting black hole which raised genuine questions about its survival.

Mr Allan arrived as the company scrambled to cut thousands of jobs, sell assets and shore up investor confidence.

Alongside Sir Dave Lewis, the then chief executive, he helped to stabilise the company, overseeing the sale of several large overseas businesses and rebuilding its market share in the UK.

In 2019, he oversaw the process of identifying Sir Dave's successor, appointing former Boots executive Ken Murphy to replace him.

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Tesco has steadily revived its domestic fortunes, and remains by far the largest food retailer in Britain.

Like its rivals, it has been grappling with the impact of the pandemic and, more recently, the rampant inflation which has gripped Britain's economy.

Its recovery has come during a period of seismic change in the industry, with Morrisons's performance faltering, the German discounters Aldi and Lidl growing rapidly and Asda being sold to the billionaire Issa brothers and buyout firm TDR Capital.

On Thursday morning, Tesco shares were trading at 260.8p, giving the company a market value of over £19bn.

Tesco declined to comment.