In a trading update today (3 April), Dawson announced the contract is expected to be terminated in the autumn and then move to Smiths News.
It follows the loss of the contracts to distribute titles on behalf of Associated Newspapers and Comag last month, worth about £140m. Both contracts expire in 2010.
Dawson has also recently lost contracts with Frontline and Seymour Distribution, two clients in the magazine distribution sector.
In a statement to the City, the group said it was "undertaking a detailed review of the implications of these contract losses".
The group added that Dawson Media Direct, which supplies newspapers and magazines to airlines, and Dawson Books, which supplies books to libraries, had traded well in the first half of the year.