The ONS puts net long-term international migration at +246,000 in year ending March 2017, down 81,000 from the previous year - a drop largely accounted for by a decrease of 51,000 in net migration of EU citizens.
Within this, 19,000 fewer citizens of the "EU8" countries, which joined the EU in 2004, migrated to the UK, while 17,000 more emigrated, yielding a net migration figure of +7,000.
Net migration from the more recent "EU2" accession countries of Romania and Bulgaria also fell, though less sharply, by 18,000 to +43,000.
In all, 275,000 people came to the UK to work, but only 87,000 came to look for work, down 39,000.
According to ONS head of international migration statistics Nicola White: "People are increasingly more likely to move to the UK or overseas only with a definite job than to move looking for work."
She added: "These results indicate that the EU referendum result may be influencing people’s decision to migrate into and out of the UK, particularly EU and EU8 citizens."
British Summer Fruits chairman Laurence Olins said: "These new figures are worrying evidence of the impact Brexit will have on EU nationals working in Britain.
"For the soft fruit industry, this confirms our own recent data which shows that in some areas up to 20% of seasonal workers are leaving our farms and returning home due to the uncertainly of Brexit and the fall of the pound against the Euro."
And he warned: "If we do not have the pickers, we do not have a soft fruit industry. If we cannot ensure access to the seasonal workers needed to produce soft fruit in Britain, that will be an unintended consequence of Brexit — along with soaring prices and increased reliance on imports.
"We are just one industry; these new net migration figures highlight a wider problem across a number of industries. We need the government to work fast to find a solution to migration once we leave the EU."