The Markit/CIPS purchasing managers' index showed activity in UK services recorded the biggest month-on-month rise in the survey's history.
At one stage the pound hit $1.3372 against the dollar, but slipped back to trade at $1.3312, a rise of just 0.13%.
Some analysts think the data indicates the UK might avoid recession later this year.
"The prospect of sterling strength is on the horizon as today's PMI figures suggest that the reported fall in activity following the EU referendum may have been a blip," said Ranko Berich, from Monex Europe.
"They do change the likelihood of a severe economic contraction in the third quarter, which previously seemed all but assured for many observers," he added.
Other analysts warned not to read too much into the latest numbers.
"These PMIs are only surveys - more hard economic data over the coming months will be crucial. It's easy to read to too much into a survey for a single month. We are not out of the woods yet," said Neil Wilson, markets analyst at ETX Capital.
The FTSE 100 was not moved much by the data. It eased lower, falling by 15 points to 6,879.
Banks weighed on the index, with Royal Bank of Scotland falling by 3.5% and Lloyds Banking Group down 2.1%.
Those shares fell after negative comments from analysts at Deutsche Bank.
Mining shares were a bright spot on the FTSE 100. BHP Billiton was up 1.3% and Randgold Resources rose 1.6%.
Shares in Marks and Spencer fell 1.4% following confirmation that it plans to cut more than 500 jobs at its head office.
US financial markets were closed for Labor Day.
(Close): The pound has lost some of the sharp gains made against the dollar after strong data on UK services.