In June, the Daily Star shifted 809,992 copies, of which just 339 were below its cover price of 20p.
Proprietor Richard Desmond then intensified the price war by cutting the Star's price in London to 10p on 5 July.
This gave its headline circulation an uplift to 843,229, although 100,033 copies were below full rate.
The Daily Mirror was down between June and July, but only by 0.5% to 1,242,446. It is down 7.3% year on year, while the Star is down 5%.
The Sun climbed by 2.1% from June back over the three-million level to 3,042,406, and is down only 2.5% year on year.
News International is discounting the tabloid from 30p to 20p in parts of the country, including London, Birmingham and Oxford, and full-rate sales were just 1,412,654.
Elsewhere in the national daily market, The Guardian sticks out for dropping to a new monthly low of 277,246 copies.
Its circulation dropped 3.1% from June and 15.7% year on year, although it has stripped out all of the 9,483 bulk copies it distributed in the UK last July.
The Independent is also close to its low, slipping 1.7% from June to 183,975 copies in July. It is down 2.7% year on year, but this masks its UK bulk copies rising from 38,498 to 62,433.
July was also a bad month for the Financial Times, which fell 3.4% to 378,497, although all titles in the quality sector dropped from June.
The Daily Telegraph fell 0.4% to 678,391, while The Times fell 0.2% to 502,588.
In the mid-market, the Daily Mail added 1.2% to reach 2,117,839 copies, while Desmond's Daily Express fell 0.1% to 663,871.
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