Full-price sales were up nearly 3%, while total sales were up 1.4% compared with the same three months last year.
The company has raised its profit forecast for the year to £365m.
But sales in Next stores have been badly affected by the pandemic and are about half of what they were by this time in 2019.
There are fears that the coronavirus pandemic is worsening in the UK, just as firms gear up for the traditionally busy Christmas period.
Next has warned that a two-week lockdown in England, Scotland and Northern Ireland in November would cause a drop in full-price retail sales of nearly £60m.
Last month, the boss of Next, Lord Wolfson, said there was a clear threat to thousands of jobs in retail, because the lockdown had triggered a permanent shift to online shopping.
Retailers have been hit hard by coronavirus lockdowns and the drop in footfall in major towns and cities, as more people work from home.
Earlier this week, US clothing brand Gap said it was considering shutting all its own stores in the UK and moving to a franchise-only model, which could cost thousands of jobs.
