The Independent, acquired by Lebedev in March, nudged up its headline circulation by 0.32%, posting 184,137 copy sales in a month.
The Independent, now edited by its former editor Simon Kelner, is expected to undergo a new strategy in the coming month as it looks to win back readers from its quality rivals.
Those newspapers, The Times and The Guardian, both fell on the month by 0.52% to 502,436 copy sales and by 0.51% to 283,063 copy sales respectively.
The Guardian's circulation has fallen in the last six consecutive months. Parent company Guardian News & Media has reduced the number of copies of the Guardian it prints in Europe.
The Daily Telegraph was up 0.22% to 686,679 but is now selling nearly 100,000 copies less than it did six months ago. All three of the quality titles suffered double digit year-on-year declines.
Across the mid-market, The Daily Mail, under the stewardship of editor-in-chief Paul Dacre, fell 1.37% between February and March to register a circulation of 2,082,352. The Daily Express fell 0.70% to 668,273.
Despite the mid-market leading Daily Mail, with a cover price of 50p, falling 5.4% year on year, its executives argued it was a strong month for the title. Circulation director Neil Jagger said: "These are difficult trading conditions for all newspapers but the relatively strong results for March clearly demonstrate our readers' loyalty and resilience during these tough economic times."
Across the red-tops, The Sun, which is still price cutting to 20p in London, registered more than 3 million readers, a slight increase on the previous month of 1.09%. But it was down 2.04% on the year to register a circulation of 3,005,308.
The 20p Daily Star was the only national daily newspaper to register a year-on-year increase, up 0.87% on the year, as it hit 827,005 copies. The Richard Desmond-owned title was also up on the month by 2.88%.