Meanwhile, the Liberal Democrats have seen their share of the student vote rise from 7 per cent to 22 per cent during the same 20-month period.
The findings come as MPs have backed a bid for a general election on 12 December.
Mr Corbyn has seen his popularity rating decrease from +35 per cent in February 2018 to just +1 per cent this month.
Ms Swinson is only narrowly behind the Labour leader at -2 per cent.
It comes after Labour has been criticised for its ambiguous position on Brexit and for inaction on antisemitism.
The data shows student support for Labour has increased slightly from 38 per cent in August to 43 per cent in October, but it is well below the 70 per cent share in February 2018.
The pro-EU Lib Dems have also seen their student support rise to 22 per cent, which suggests the party is winning back favour with young voters following their U-turn on scrapping tuition fees in 2010.
The Greens are on 14 per cent while the Conservatives have slipped down to 11 per cent.
Josephine Hansom, from YouthSight, said in a blog post: “The Lib Dem brand has been largely detoxified since the damage they experienced after the 2010 student fees debacle. This is a very recent change.
Nick Hillman, director of think tank Higher Education Policy Institute (Hepi), told The Independent: “I think the sheen has faded on Jeremy Corbyn for many students while the Lib Dems are looking more attractive to them again.
“There’s lots of reasons, including the rows about racism in the Labour Party. In addition, Jeremy Corbyn is no longer the new kid on the block, as Jo Swinson has taken that crown.”
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