The company, owned by Associated British Foods, said value and unit sales data from Nielsen for the 12 weeks ending 6 July 2013 placed it number two in the bakery pecking order behind Warburtons.
It also said that Kingsmill is now the number two bread brand in the UK.
Mark Fairweather, chief executive of Allied Bakeries, said: "Over the past few years we have followed a plan focussed on building a strong, sustainable bakery business as we’ve invested in our brands, our bakeries and our ways of working.
“We’re seeing the benefit of that work as we build stronger relationships with our customers and take on new business with new customers such as the contract to supply Kingsmill, Allinson and Burgen bread to over 4,000 Co-operative Food stores.
“I’m delighted to be able to confirm that one of the results of our hard work is that the growth we’ve seen has moved us to the number two position in this highly competitive market.
"This new partnership with the Co-operative is now an established part of our total operation and a credit to the hard work of all our colleagues.
“Our investment in infrastructure, innovation, brands and people – the largest capital expenditure programme in UK bakery - sees us operating on a significantly stronger platform than ever before."
The company’s latest stage of this investment is the opening of a new bread line at its Walthamstow plant. This new breadline will manufacture Kingsmill 50/50, Soft White and Tasty Wholemeal, with a capacity to produce 10,000 loaves per hour. The line comes equipped with new ovens, provers, coolers, and bagging and slicing equipment, as well as a revamped dispatch area.