By Sumanta Dey

(Reuters) - Euro zone business growth held steady in June, but the modest pace suggested economic growth in the second quarter was half the rate of January-March, even as a rebound in Italy and rapid acceleration in Spain brightened the outlook.

In France, the euro zone's second largest economy, data showed both services and manufacturing contracting.

The majority of the surveys were completed before Britain voted on June 23 to leave the European Union, meaning the after-shocks of the referendum have yet to be reflected in the data.

Of ongoing concern to policymakers at the European Central Bank, whose years of ultra-easy monetary policy has failed to boost inflation anywhere close to its 2 percent target ceiling, is that firms were still slashing prices to drum up business.

Markit said its latest composite Purchasing Managers' Index for the euro zone, steady at 53.1 in June, pointed to GDP growth of 0.3 percent between April-June, just half the 0.6 percent rate clocked in the first quarter.

But there were some notable bright spots in the data.

Italian businesses returned to growth, and a surge in Spain's service sector, where firms hired faster in June than in any month since 2007, means the bloc's third and fourth largest economies may be finally beginning to pull some weight.

Spain's unemployment rate, at 21 percent in the first quarter, is among the highest in developed economies.

"Euro zone PMIs were consistent with moderate economic momentum but it is too feeble and the risks to the economy have tilted to the downside because of Brexit," said Philip Shaw, chief economist at Investec in London.

"But does the Brexit vote result in a completely different world economy in the second half of this year? Our view is that it would change the state of the UK economy, but not do much to the euro zone or the rest of the world."

Euro zone retail sales, a proxy for household spending, rose 0.4 percent in May, its highest monthly increase this year on surging demand for non-food products.

In Germany, Europe's largest economy, retail sales on a monthly basis rose 0.9 percent after two consecutive falls, while in France, sales remained flat.

Among the PMIs for the euro zone's two largest economies, German private sector growth eased in June and French activity stagnated as waves of strikes last month weighed on output, alongside a clear trend of price discounting.

A sub-index measuring prices charged held stubbornly below the 50 mark that separates growth from contraction. The euro zone just escaped deflation in June for the first time in five months, with prices up 0.1 percent on a year ago.

New business, however, continued to grow throughout the currency bloc and employment picked up considerable pace in the euro zone as a whole, as well as Spain and Germany.

Across the English Channel, British services activity slowed to a three-year low and sent business expectations to their weakest since the end of 2012, in the run-up to the EU membership referendum.

The UK services PMI eased to 52.3 in June from 53.5 in May.

Coupled with the latest data, manufacturing and construction PMIs in the UK pointed to economic growth of 0.2 percent in the second quarter down from 0.4 percent in the first three months of 2016, Markit said.

A Reuters poll conducted soon after votes were counted on June 24 found Britain's economy would slip into recession and the Bank of England would be forced to cut interest rates.

(Editing by Ross Finley and Raissa Kasolowsky)