The Independent on Sunday was among the worst performers, losing 14.8%. Sunday Sport, which underwent a revamp earlier this year, lost 19.2% of its circulation in the 12 months to June. The People suffered a 13.1% decline.
However, there could be signs of recovery for The Independent on Sunday, which cut its price from £1.80 to £1 last month. Its June ABC figure was up 4.3% from May.
Meanwhile, Scottish papers Sunday Herald, down 4.3% month-on-month to 45,455, and Scotland on Sunday, down 2.8% month-on-month, were also big losers.
Elsewhere in the Sunday quality sector, The Observer lost 3% of its circulation last month, compared with last June, while The Sunday Telegraph shed 3.1%.
Among the red-tops, Sunday Mail and Sunday Mirror posted year-on-year drops of 4.8% and 5.3% respectively. However, News of the World and Daily Star Sunday both posted higher ABCs last month than in May.