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.

Spurs, who are having a new £400m stadium built next to their existing home White Hart Lane, could also play next season's home Champions League games at the national stadium.
They aim to move into their new 61,000-seat home before the 2018-19 season.
"We're a long way down the path on reaching an agreement," Dyke said.
"I think there's some discussion about whether they'll play their Champions League games there at Wembley next year but I don't know much about that."
Tottenham's north-London rivals Arsenal hosted Champions League games at Wembley in 1998-99 and 1999-2000.
Dyke also said Chelsea could play home games at Wembley in the near future.
The Blues have plans to redevelop Stamford Bridge, which could leave them needing a temporary home for several seasons.
"I think Chelsea might come for a longer period," he told Sky Sports News HQ. "Chelsea have got really exciting plans for their stadium. They're going to demolish the whole thing and build a whole new stadium on the existing site.
"If they came to Wembley, that would mean them coming for three years."
(Close): The pound has lost some of the sharp gains made against the dollar after strong data on UK services.
[NEXT_CONCEPT]
Tottenham are close to a deal to play home games at Wembley in the 2017-18 season, says Football Association chairman Greg Dyke.