And for the year overall, the economy could grow at its fastest pace since 2007, the last of the boom years before the financial crisis struck.
The immediate effect was felt in the jobs market – the firms reported hiring more staff in June than at any time in the 22-year history of the survey, run by Markit.
Its purchasing managers’ index (PMI) came in at 57.7 in June – a slowdown on the 58.3 in May, but still strongly above the 50 level which indicates no growth.
Economists believe the figure points to very healthy GDP growth in the second quarter of the year.
RBS analysts forecast growth of 0.9 per cent, up from 0.8 per cent in the first three months of the year and the strongest quarter since mid-2010.
Markit found 27 per cent of services firms took on more staff in June, a positive indicator for growth through the rest of the year.
“With the survey having seen new record rates of job creation in each of the past three months, unemployment should continue to plummet in the second quarter from the 6.6 per cent rate seen in the first quarter,” said Markit’s chief economist Chris Williamson.
“A jobless rate below six per cent is achievable by the end of the year if anything like the current pace of job creation is sustained in the coming months.”
Previously, growth had appeared to be based strongly on house price growth and rising consumer spending.
But economists are increasingly hopeful that business investment is also bouncing back, supporting a more sustainable recovery.
Analysts at Citigroup believe the economy could grow by as much as 3.5 per cent this year, a post-crash high, with fixed investment soaring by 9.8 per cent.