The London Retail Consortium said the growth was a good gain on top of the 5.3 per cent year-on-year increase in June last year.
However, like-for-like sales in Central London achieved slower growth in the second quarter, from April to June, than the previous one - up 7.3 per cent, compared with 8.7 per cent in the first quarter.
The LRC pointed out that retail footfall last month was lower than in June last year, but added: 'The wet weather and clearance Sales did attract customers who continued to spend more, albeit on fewer trips.'
Visitor numbers remained higher than a year ago and tourist spending was slightly stronger than in May.
LRC director Kevin Hawkins: 'This is a good result, reflecting the continued recovery in overseas tourist footfall that began last year.'
But Hawkins warned: 'It also reflects the decision by several West End stores to bring forward their July clearance Sales into June, so the comparatives look better than they otherwise would have been.'
Last month's heavy rainfall slowed sales of clothing and footwear, particularly at high street retailers. Top-end ranges maintained their strength, as did designer handbags, jewellery and watches.
Homewares sales were mixed and largely driven by discounting, but performance varied at difference stores and across different sectors. Furniture and big-ticket items performed well for some, but others noted signs of consumer caution.