According to the government's own report, it did not. The meddling was insubstantial
Do you wonder why there even was a referendum?
Compare 1997: Sir Jammy Fishpaste hates Europe, spends millions of his own money promoting his Referendum Party, gets nowhere. Because it's "cool Britannia" and the common man is doing well for himself. People think he's a nutter and all he achieves is keeping 4-11 Tories out of power by sapping their votes
But the 2008 crash wrecks the country. UKIP builds a voter base over years, and gets an enormous share of the vote. That's a warning shot for the Tories, whose voters UKIP are sapping. They only just squeaked through a hung parliament with a Libdem coalition. Hence Gambling Dave offers a referendum to bring Europe haters back to his party so he can remain in power.
Those percentage points were already in place before Russia even got going.
Yep, working class people's lives have sucked after 2008, though it was a continuation of a longer trend and is still continuing. (And COVID made it worse. All us tech people sitting comfortable in our home office while mass wealth transfer happened out of blue collar pockets...)
Worth remembering... Anti-globalization and anti-liberalization were slogans and policies of the socialist left in the late 90s and 2000s. Battle of Seattle, Occupy, etc. Voices marginalized and mocked by the neo-liberal centrist "left" (not left) in the Democratic party, Labour party, mainstream European govt's, Canadian Liberal party, etc. Manufacturing jobs were dumped overseas, union membership declined, middle class incomes plummeted, 2008 drained people's financial well being, while housing prices skyrocketed etc. And same "moderate" forces also went to war in the middle east, etc. etc.
Obama ran on left populist slogans but actually governed from the neo-liberal centrist right.
Actual socialist left voices and formerly moderate social democratic policies generally had no voice or power in government anywhere, Corbyn was run out of the room, Bernie isolated, etc.
So it's no surprise that the right and far right saw the vacancy and exploited it. The rise of Trump, of UK Reform, etc. ties directly into this sense of hopelessness and anger people had.
Now the "conservative" right -- which was formerly pushing liberalization the strongest -- talks in angry tones about "globalism" instead of "globalization", and it's caught up with anti-Semitic dog whistles, national chauvinism, etc. etc. That shit sells.
The Russia report? It says that they didn't seek to assess Russia's impact?
Farage was basically a Putin asset, for years; I don't doubt that a lot of the sentiment was there before any influence, but to my recollection the influence was obvious and very heavy