The report on business trends from the accountancy and services group BDO said the UK economy was already showing signs of slowing ahead of the EU vote.
Manufacturing had the gloomiest outlook, and job creation in the economy slowed to a two-year low.
BDO's Peter Hemington said uncertainty prompted by Brexit had also disrupted investment in the UK economy.
The report shows business output, which reflects company orders for the next quarter, slipped to 99 last month, compared with 99.7 in May and 100.6 in April.
Meanwhile, business optimism also slid, falling to 98.9 in June from 99.4 in May.
But Mr Hemington added: "In all likelihood, whatever arrangements the UK eventually arrives at with the EU won't look very different from what we have at the moment.
"So businesses cannot afford to get caught up in the hysteria. They need to hold their nerve and continue to invest in the UK.
"We are at a crucial moment where we must be sensible in protecting the UK economy. We need a plan of action now that gives businesses the added confidence to progress with investment plans."
BDO's research is based on the results of the UK's main business surveys

Mr Trudeau toasted the two nations as "siblings" at a state dinner.
Mr Obama raised his glass at the White House to the "great alliance" and joked about Mr Trudeau's previous jobs.
"If things get out of hand, remember the prime minister used to work as a bouncer," said Mr Obama.
In a joking reference to Canadian-born presidential candidate Ted Cruz, Mr Obama said: "Where else could a boy born in Calgary run for president of the United States?"
A lavish state dinner was held for Mr Trudeau and his wife Sophie Gregoire-Trudeau, featuring poutine, Nanaimo bars and white chocolate snowballs.
During Mr Trudeau's toast, he referred to the 25,000 refugees from Syria who have arrived in Canada in the past four months, saying that "diversity can be a source of strength".
More than half of US governors oppose allowing refugees to settle in their states.
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After a private meeting at the White House, Mr Trudeau said he had learned a lot from "my friend Barack", who he described as "a man of both tremendous heart and tremendous intellect".
Earlier, Mr Obama said the two leaders share "a common outlook" and that Mr Trudeau had brought "new energy and dynamism not only to Canada but to the relationship between our nations".
He added that the US and Canada were "blessed to be neighbours".
The leaders have pledged co-operation on liberalising investment and trade, promoting clean energy and preventing foreign fighters from travelling to the Middle East.
Mr Trudeau came bearing gifts for the First Family: a pair of Canadian-made dog boots called "Muttlucks" for the pet dogs, a beaded cape for Mrs Obama, an aboriginal statue for Mr Obama, and scarves for the president's daughters.
Ahead of the meeting, a joint statement on environmental cooperation announced that the US and Canada would cut methane emissions by 40-45% below 2012 levels, by 2025.
They also agreed to set "world class" standards on commercial activities in the Arctic, including oil and gas exploration.
US-Canada relations had previously suffered because of energy issues, when Mr Obama's administration opposed the Keystone XL pipeline, which was meant to transport oil from Canadian tar sands in Alberta to the US Gulf coast.
President Obama, 54, sees in the young leader a man who shares his progressive politics, as well as his early rhetoric of hope and change, the BBC's Barbara Plett-Usher reports from Washington.
Mr Trudeau's optimistic election platform has led many to draw comparisons with the beginning of Mr Obama's presidency and some American liberals to draw envious comparisons with the US's political scene.
As Donald Trump solidified his position as front-runner for the Republican presidential nomination earlier this month, there was even a spike in internet searches about how to move to Canada.
In Washington, Mr Trudeau chose his words carefully after being asked by reporters for his views on US-Canada relations under a Donald Trump or Ted Cruz presidency.
He said he looked forward to working with whomever US voters elected to the White House.
Uncertainty around Brexit has dragged UK business output and optimism to three-year lows, a report suggests.
[NEXT_CONCEPT]
US President Barack Obama and Canada's new Prime Minister Justin Trudeau have lavished praise on each other during the first official visit by a Canadian leader in nearly 20 years.