Norman Baker, Liberal Democrat candidate for Lewes, has written to Trade and Industry secretary Stephen Byers asking him to re-open the inquiry into whether Desmond is fit to run a newspaper.
Baker's calls come after Sunday Express editor Michael Pilgrim wrote a memo to Desmond accusing him of suppressing legitimate stories for commercial reasons and to "settle scores".
The memo says, "I have been asked on several occasions to suppress evidence of wrongdoing. I have been asked to suppress stories for "commercial reasons" which have not in the slightest benefited newspaper. I have been under pressure to run unjustified stories to settle scores."
Pilgrim goes on to warn Desmond that if this behaviour continues "the paper will not be taken seriously".
When Desmond bought the Daily Express, Sunday Express and Daily Star in November he pledged not to interfere in editorial decisions.
It has also been discovered that Desmond made a £2m payment to New York mafia family the Gambinos after they failed to reap profits from adverts they had placed in Desmond's porn magazines.
A spokesman for Desmond said that Desmond had never knowingly engaged in business dealings with people associated with organised crime, directly or indirectly.