Like-for-like sales were up 0.3% in the 13 weeks to 28 May, with sales of fruit, vegetables and meat up by 5% more than overall sales.
"Our new fresh food brands are performing very well, with over two-thirds of our customers having bought products from the new range," comments chief executive Dave Lewis.
In branding its fresh produce with made-up farm names earlier this year, Tesco was following the lead of budget supermarkets Aldi and Lidl. Names include 'Woodside Farm', 'Willow Farm' and 'Boswell Farm' - none of which actually exist.
However, the strategy was slammed by the farming industry.
"There will inevitably be shoppers who are led to believe that the fictional names of the farms are the real source of the product - this makes the need for clear and accurate origin labelling even greater, said Ruth Mason, chief food chain adviser for the National Farmers' Union (NFU)."
However, the strategy has clearly worked - either because customers aren't aware that the British-sounding produce is nothing of the sort, or because they don't care.
"After all, the strategy is similar to that employed by Aldi and suggests that for most shoppers, the perception of provenance is sufficient, provided the products are perceived to be good value."
Tesco claims that its prices are now 6% lower than in September 2014. Like Sainsbury's, it has cut back on multi-buy offers and vouchers in favour of lower shelf prices.
"Sales are still being pegged back by food deflation, as supermarkets fall over themselves to cut prices in an attempt to win back market share from Aldi and Lidl, says Laith Khalaf, a senior analyst with Hargreaves Lansdown.
But, he adds, "The elephant in the room is Amazon, which is currently testing out a grocery delivery service for some customers in London; if successful this represents a clear and present danger to the health of UK supermarkets."
Tesco has also consolidated its business in recent weeks with the sale of its Dobbies Garden Centres chain and restaurant chain Giraffe. It has now announced plans to get rid of its Harris & Hoole coffee shop chain as well, which will be sold to Caffe Nero.
"Together, these sales allow us to place even greater focus on our core UK business," says the firm.