The Barclay brothers-owned Telegraph registered its second successive monthly increase, taking it off its low of 447,428 copies in May.
It is the second best-performing national Sunday quality paper in year-on-year circulation performance, limiting its decline from July 2011 to 9%.
The Sunday Times and The Observer also achieved small rises from June, although The Independent on Sunday dropped 3.1% to 118,759 copies.
The reporting period, 2 July to 29 July, included the first Sunday after the start of the Olympic Games.
Outside the qualities, only The People's circulation climbed from June, with a 1.99% rise taking the Trinity Mirror title to 459,032 copies.
The Sun on Sunday dropped 1.5% to 2,147,482 copies, though its rate of decline since its launch at the end of February with 3,213,613 copies, continues to level out.
The Sunday Mirror was also hit, dropping 1% to 1,077,882 copies, but the Daily Star Sunday was the worst performer, down 3.6% to 456,429 copies.
In the mid-market sector, The Mail on Sunday lost 2.5% of its June circulation, leaving it on 1,779,449 copies, down 21% year on year.Follow @DanFareyJones