The 62-year-old told The Yorkshire Post that he plans to open 20 new Community Shop stores over the next three to four years.
Mr Marren is the country’s largest distributor of surplus food through his established network of stores and websites for factory workers.
His Community Shop concept offers surplus food and support services for people who are living in poverty and want to change their lives.
He launched the first social supermarket in the former mining village of Goldthorpe near Barnsley in 2013 and opened a second in South London in December.
The model is well established in Europe, with around 1,000 stores.
Mr Marren said he has had enquries about opening 175 Community Shops across the UK and Channel Islands.
He said the need for the shops has “absolutely” increased since the economic downturn. “You only have to look at figures for food banks,” he added.
The Trussell Trust charity claims that numbers turning to foodbanks are continuing to rise despite economic recovery, and more people are struggling to get by because their incomes are too low.
Mr Marren said he is in discussions with local authorities and food producers about setting up stores in areas of high deprivation.
He added that the first Community Shop has had “great results” in Goldthorpe and is providing enough food for thousands of meals a week for its 750 members and their families.
The Lambeth store has won high-profile backing from London mayor Boris Johnson who described it as a “sterling example of social enterprise and private organisations working together to create positive outcomes”.
Mr Marren said: “We are only scratching the surface at the moment. We have some great things to do. We are currently moving more than 30,000 tonnes of surplus product a year. We are looking to double that over the next three years.
“We believe the figure of surplus food that could go back is around 300,000 tonnes.”
He said he has “tremendous support” from major food retailers which are diverting surplus food to the initiative. They include Asda, Marks & Spencer, Morrisons, Nestle, Ocado, Tesco and Waitrose.
The group sells food that is wholesome and within date at discounts of up to 70 per cent.
The Community Shop also offers debt advice, cookery skills, home budgeting and CV writing services to members.
Mr Marren started his business career with £300 at the age of 19 at a grocery in Tankersley in 1973. He started supplying hospitals, local authorities and polytechnics and other low-cost catering providers and expanded his range as his early suppliers diversified from frozen foods into chilled and ambient categories.
The group has 18 stores and 15 websites selling surplus food to workers in factories and the emergency services.
Its management team includes Sarah Dunwell, the former chief executive of pioneering Leeds social enterprise Create, and Tom Rumboll, a former relationship director at Lloyds Banking Group.
In 2013, the Company Shop Group had sales of £27.6m and earnings before tax, debt and amortisation of £2.2m.
It employs 582 people and Mr Marren is the sole shareholder.
Family values at heart of business
John Marren said he founded his company on family values, “where employees are part of everything you do”.
The Company Shop Group won a Queen’s Award for Enterprise last month for its “outstanding achievement” in sustainable development thanks to its ongoing work to “ensure a better quality of life for everyone, now and for generations to come”.
Mr Marren said the award was due to the efforts of the employees. He added: “I am looking forward to the presentation where we can celebrate the success together.”
Mr Marren is due to attend an awards event at Buckingham Palace in the summer.