The figures, from retail analyst IGD, indicate that 29% of consumers expect to do more of their shopping at discount stores over the next 12 months, up from 25% last month.
Other findings of the survey include that nine in 10 consumers think food price will continue to rise of the net year and that a further 15% of shoppers intend to fight back by buying more from frozen food specialists, such as Iceland and Farmfoods.
Joanne Denney-Finch, IGD chief executive, said: "The vast majority of shoppers believe that food inflation is set to increase over the next 12 months. They are not taking it lying down and instead are prepared to sacrifice some of their time by shopping around at different retail formats, from discounters to frozen food stores, to get the best deals."
Hitting the discount stores is not the only way to minimise the cost of your weekly shop, though. Cashback sites such as Quidco and Top CashBack, for example, can prove a massive help for families keen to reduce their outgoings.
Most online purchases from M&S also qualify for 5% cashback for those who log on to the M&S site through Top CashBack, while new Top CashBack members can get £15 off their first £50 online grocery shop at Tesco.com.
If you are happy to buy in bulk, Shorters Club, which offers groceries, fresh and frozen produce at wholesale prices, can also help you to make huge savings on items such as loo rolls and cereals.
And Amazon's Grocery section is currently offering some fantastic back-to-school deals such as 59% - or £6.70 - off the retail price on a five-pack of 500g boxes of Shreddies.
What's more, with surging petrol prices taking the toll on drivers, shopping online is a great way to keep transport costs down - and avoid those impulse purchases that can push your bills through the roof - too.