LONDON, (Reuters) - Britain's economy looks set for a significant slowdown after a strong second quarter, a think tank said on Thursday, based on data mostly recorded before last month's decision by voters to leave the European Union.

The warning from the National Institute of Economic and Social Research (NIESR) follows some early signs that businesses and consumers might be suffering from uncertainty created by the June 23 vote to leave the EU.

NIESR estimated Britain's economy expanded 0.6 percent in the second quarter, up from a 0.4 percent increase in the first three months of the year.

But it warned the acceleration was driven by a surge of activity in April, adding that gross domestic product likely stagnated in May and contracted in June.

"What it does suggest is that when April drops out of the three-month calculation we should see a quick deterioration of growth, especially if the estimated contraction in June persists or accelerates into July and beyond," Jack Meaning, a research fellow at NIESR, said.

The Bank of England has taken steps to ensure British banks keep lending as the financial consequences of the referendum decision began to materialize, especially in commercial real estate.

Governor Mark Carney has said he expects the Bank to pump more monetary stimulus into the economy over the summer.

Surveys of British firms published by Markit/CIPS, conducted mostly before the June 23 referendum, suggested Britain's economy is growing at a quarterly pace of just 0.2 percent.

A YouGov/CEBR survey on Tuesday showed business confidence dropped sharply after the referendum result.

NIESR warned before the June 23 vote that Britain's economy would likely end up around 1.0 percent smaller in 2017 in the event of a Brexit vote than if the country decided to stay in the EU, and would be 2.3 percent smaller in 2018.

((Reporting by Andy Bruce; editing by William Schomberg))