Burberry said that retail sales rose by 9pc to £370m in the three months to the end of June, with comparable sales - effectively like-for-like sales - up 12pc.
In addition, SuperGroup, the owner of Superdry, reported a 3.2pc rise in like-for-like sales for the last year, while at the discount end of the clothing market Primark said that sales rose by 22pc on a constant currencies basis in the 16 weeks to June 21.
However, Burberry said that at existing exchange rates there will be a "material" impact on profits from the strong pound. The company warned retail and wholesale profits would be reduced by £55m. The pound is trading above $1.71, a six-year high.
Associated British Foods also cautioned that its businesses, which sell sugar and grocery ingredients as well as Primark's cut-price clothing, would see profits reduced by £50m compared to last year due to movements in currency.
Primark, SuperGroup and Burberry are leading a charge of British fashion brands expanding overseas. Primark is preparing to open its first US store in Boston in 2015.
Christopher Bailey, chief executive and chief creative officer of Burberry, said: "This first quarter performance reflects our focus on striving to give customers the best possible experience of the Burberry brand through ongoing investment in retail, digital and service, both on and offline.
"The 12pc increase in comparable sales demonstrates our teams' success in unlocking the benefits of these investments, as we continue to concentrate on the things we can control in an uncertain external environment."
The "uncertain external environment" referred to by Mr Bailey, who faces an investor rebellion over his pay at Burberry's annual meeting on Friday, includes the strength of sterling.
Meanwhile, although SuperGroup reported an increase in sales, pre-tax profits for the year to from £51.8m to £45.2m. Shares in the retailer slumped in May after SuperGroup warned that like-for-like sales had fallen in the final quarter of its financial year.
However, Julian Dunkerton, chief executive, insisted the results represented a "solid performance"
He added: "With a strong pipeline of new stores, particularly in mainland Europe, we are well positioned for further profitable growth in the year ahead.
"The strength of the Superdry brand and the investment we have made in our business leaves me confident in our ability to implement and deliver the growth strategy."