The claims appears historically correct at least for elections since 1918, given this (official) graph:
One of the low points in the graph, the February 1974 election, which brought minority Labour government in power, had the popular vote breakdown as 37.9% Conservative and 37.2% Labour. Labour had won more MPs, but still short of a majority of seats.
On the other hand, in the 2015 election the Conservatives won a majority (of 12 seats) with just 36.9% of the popular vote.
So the margin by which this history claim is correct is pretty small if we take the (current) Conservatives vote share reaching 35%.
Finally, if I'm also permitted a comment on the inference from the news piece, given that Farage set out the terms under which his party won't contest the seats that the Conservatives could win (basically he just called Johnson to embrace a no-deal Brexit), and given the share of the voting intention for Farage's party is around 15% (again from the Yahoo news piece), concluding that Conservatives cannot win a majority in the current circumstance seems rather tenuous. For more context, in 2015 Farage's party did contest the election and won 12.6% of the popular vote, but only one seat.