Online sales mainly drove the increase, jumping by 48.5% in the quarter.
Tesco said its customers had been making fewer trips to its supermarkets during lockdown but had been doing bigger shops when they visit, with the amount being bought rising by nearly two-thirds.
Tesco has announced its total sales increased by 8.2% to £13.4 billion in the first sales quarter of 2020, but it warned that coronavirus-related costs were set to hit £840 million this year.
Shopping frequency fell by 32% in the 13 weeks to 30 May, Tesco said on Friday, but basket size jumped by 64%.
But a boost in sales volume for Tesco has been counteracted by the increased costs and logistical challenges of operating during the pandemic, and it reiterated a flat profit outlook. They stemmed from featuring 12 weeks' paid leave to 26,000 vulnerable staff and recruiting 47,000 short-term staff to include illness and satisfy demand from customers.
"We have also incurred costs in areas such as distribution, where we have needed to re-open previously mothballed distribution centres and property, where we have incurred costs to adapt the store environment and temporarily lost tenant income". In total, our latest estimate of incremental costs for the United Kingdom for the full year is approximately £840 million.
Dave Lewis, Tesco's chief executive, said: "Through a very challenging period for everyone, Tesco colleagues have gone above and beyond, and I'm extremely proud of what they've achieved".
Tesco said it doubled its online capacity over a five-week period to help support vulnerable customers unable to go to its stores due to the outbreak.
Like many of its rivals, Tesco was forced to overhaul its strategy in-store and online amid the coronavirus lockdown.
It also estimated a hit of £840m from the costs of dealing with the pandemic, offset in part by higher food sales and £585m of business rates relief from the United Kingdom government.
The company said it expected current year retail operating profit to be at 2019/20 levels on a continuing operations basis.
AJ Bell investment director Russ Mould thinks Tesco's efforts during the pandemic so far in increasing online deliveries, ensuring it keeps shelves stocked with items people need, and providing employment to people who've suddenly found themselves out of work, could result in greater customer loyalty down the line.
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