However, this is against a weak comparative in June last year, when sales dropped 0.5 per cent.
The World Cup had a mixed effect - reducing footfall on England's match days but boosting sales of food, drink, sportswear and large TVs. June's hot weather also helped food, DIY and gardening sales.
Overall clothing and footwear sales declines were the worst since last October, with menswear and childrenswear sliding most.
The three-month like-for-like rate of growth rose to 4.1 per cent, from 2.7 per cent in May. Total sales for April to June were up 6.8 per cent.
BRC director general Kevin Hawkins said: 'June was not as good as May. Although the gain is encouraging, much of the growth, especially in housing-related sectors, remains discount driven. Consumer confidence is still fragile and retailers will be hoping factors beyond their control do not weaken it further.'