Mr King, who led a turnaround in profits and sales during his decade in charge, told shareholders at the company's annual general meeting in London yesterday he wanted to avoid following the example of other chief executives who had outstayed their welcome and caused "difficulties" in their wake.
He also revealed the UK's fourth largest supermarket will be putting greater store by its Edinburgh-based banking arm following the deal earlier this year to buy out a 50 per cent stake owned by Lloyds. Mr King promised the group would step up its marketing drive for Sainsbury's Bank after admitting the vast majority of customers were not even aware that Sainsbury's offered financial products.
He said: "The reason we are so excited about the bank is that it is already growing as a business, with the lowest level of customer complaints out of any UK bank, but the vast majority of customers don't know we have a bank but say they would be interested in using its products and services. That represents a fantastic opportunity for us."
Mike Coupe, who has now taken on the top job, said he was "confident" the group's prices were competitive, dismissing a shareholder's claim low-cost supermarkets were "trendsetters" while bigger players have become "followers".
Mr Coupe said: "This is an intensively competitive market now [but] that has always been the nature of market, for as long as I have been in industry. Our basics range offers the lowest prices in market and we have built the Sainsbury's brand on competitive pricing. I am very confident about our current pricing point."
However, shareholder John Farmer warned shareholder returns, estimated to be 85 per cent over the past ten years, could weaken amid complacency about the company's profitability.
Sainsbury's, which has 82 stores in Scotland, made a £898 million pre-tax profit in the 12 months up to 15 March this year, but there was a 3.1 per cent sales slide in the final quarter of 2013, breaking nine years of continual growth. That was followed by a 1.1 per cent fall in the first quarter of 2014.
Mr Farmer said: "There is a risk that you will fail to compete and we should remember that the five-year shareholder return has only been 40 per cent, less than that of M&S, and discounters are gnawing at your heels."
Chairman David Tyler said the FTSE 100 company was "deeply concerned" about future returns for shareholders, adding that food retailers were "deeply out of favour in the stock market".
He added: "We have been severely affected in the wrong direction and that has affected figures. We are determined over the coming years to improve our returns and give shareholders what they want."
The chain has already made a major concession to the price war by entering a joint venture with Netto, the Danish discount store. The deal will see Netto come back to UK shores and open 15 trial stores in the North of England with support from Sainsbury's.
Sainsbury's also defended itself against heated allegations at the AGM that it was using suppliers involved with Israeli settlements. It resisted calls to boycott products made by SodaStream, a soft drinks machine company that operates in the occupied West Bank. Mr King said the supermarket does not source own-brand products from Israeli settlements and that putting both Palestinian and Israeli produce on the retailer's shelves "was the right thing to do".