Unlike the Audit Bureau of Circulations (ABCs), which monitors the number of newspapers sold, the NRS surveys a panel of 36,000 people to estimate how many readers newspapers have.
The Daily Telegraph had an estimated readership of 1.8 million a day in the year to September, down 10% on the year, despite its high-profile exposé on MPs' expenses.
The Independent's readership dropped 12% to 636,000, while The Guardian fell 8% to 1.14 million, and The Times nudged up 2% to 1.8 million.
The statistics contrast markedly in some cases with ABC figures. For instance, in October, The Times registered an ABC of 571,783 compared to The Telegraph's 767,894.
According to NRS, the big winner across the quality press was Pearson-owned Financial Times, up 12% to 433,000.
Across the red-tops, The Sun had an estimated readership of 7.8 million, the Daily Mirror 3.4 million and the Daily Star 1.5 million.
The NRS pointed out it was 95% confident the data for The Daily Telegraph and Daily Mirror was subject to a real change in readership habits. It added that the other changes could be due to sample variation.