Data from IHS Markit’s Purchasing Managers’ Index, or PMI, shows a fall to 47.7 in July, the lowest level since April in 2009. A reading below 50 indicates contraction.
Both manufacturing and service sectors saw a decline in output and orders.
However, exports picked up, driven by the weakening of the pound.
The report surveyed more than 650 services companies, from sectors including transport, business services, computing and restaurants.
It asked them: “Is the level of business activity at your company higher, the same or lower than one month ago?”
It also asked manufacturers whether production had gone up or down.
The PMI is the first significant set of data measuring business reaction to the result of the UK referendum.
Chris Williamson, chief economist at IHS Markit, said the downturn had been “most commonly attributed in one way or another to ‘Brexit’.”
He added that the economy could contract by 0.4% in the third quarter of this year, but that would depend on whether the current slump continued.
“The only other times we have seen this index fall to these low levels, was the global financial crisis in 2008/9, the bursting of the dot com bubble, and the 1998 Asian financial crisis,” Mr Williamson told the BBC.
“The difference this time is that it is entirely home-grown, which suggest the impact could be greater on the UK economy than before.
“This is exactly what most economists were saying would happen.”
‘Heading for recession’
Samuel Tombs, chief UK economist at Pantheon Macroeconomics, said the figures provided the “first major evidence that the UK is entering a sharp downturn”.
Although he added that the “confidence shock from the Leave vote might wear off over the coming months”.
Neil Wilson, markets analyst at ETX Capital, said he thought the UK was “heading for a recession again”, and that the data would almost certainly prompt the Bank of England to roll out further stimulus.
The pound has fallen in response to the publication of the data.
The UK’s new chancellor, Philip Hammond, urged caution.
“Let’s be clear, the PMI data is a measure of sentiment, it’s not a measure of any hard activity in the economy.
“What it tells us is businesses confidence has been dented, they’re not sure, they’re in a period of uncertainty now.”
Earlier on Friday, Mr Hammond said that he might “reset” Britain’s fiscal policy.
While IHS Markit’s reading on the UK economy was worse than most analysts expected, its verdict on the wider eurozone economy was more cheery.
Although business confidence dropped to an 18-month low, the overall pace of economic growth was in line with pre-Brexit trends, and employment across the eurozone rose.
The optimistic outlook is in line with comments made by the president of the European Central Bank (ECB), Mario Draghi, who said on Thursday that Europe’s financial markets had “weathered” the uncertainty caused by the vote.
Europe Economics’ Andrew Lilico, who argued during the referendum campaign that leaving the EU would be beneficial for the UK in the long term, told the BBC the PMI data was “no surprise”, and that it “doesn’t tell us much about what Brexit’s longer term impact will be”.
Mr Lilico said he always expected a short-term reaction, and those who voted to leave, “expected a short-term slowdown too”.
The downturn, he added, was “associated with risks in the global economy,” as well as Brexit.