Deliveroo saw a 59% growth in orders in the UK and Ireland between July and August this year despite the reopening of restaurants for dining in.
The delivery firm received 35.8 million orders during the three month period, compared to 22.6m in the same quarter last year.
The overall gross transaction value of its orders rose 56% to £852m, although there was a £68m drop on the previous quarter which Deliveroo blamed on "typical seasonality".
Deliveroo founder Will Shu said the company's strong performance had been boosted by a partnership with Amazon to offer Prime customers access to its Deliveroo Plus subscription programme, which has more than doubled its membership as a result.
It also benefited from the launch of a rapid grocery delivery service with Morrisons in September.
Deliveroo has upgraded its full-year growth forecast following a sharp rise in the value of its orders across its entire international business.
The delivery firm said the overall gross value of its orders across all markets rose 58% to £1.59b year-on-year in the third quarter of 2021 despite lockdown restrictions easing in most regions.
It said it expected its full-year gross transaction value to rise by 60%-70%, up from its previous forecast of 50%-60%.
Shu said: "While we are mindful of current and potential macroeconomic disruptions and uncertainties, we expect further strong performance in the remainder of the year and we are increasing our full year [gross transaction value] growth guidance.
"We remain excited about the opportunity ahead and our plans to deliver better value to our consumers, help our restaurant and grocery partners to grow, and provide further opportunities for riders."
The number of Deliveroo's active customers rose 56% during the quarter while overall order numbers increased by 64%.
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