Sky, which is being sued by the cable operator in a complaint over carriage fees, had been ordered in an earlier court hearing to let Virgin's lawyers see a number of confidential business documents as they prepare their case ahead of a trial next year.
It is understood that the satellite company wishes to withhold the vast majority, more than three quarters, of the documents requested by Virgin.
According to a Daily Telegraph report, Sky has raised concerns about a possible conflict of interest because Virgin's lawyers, Ashursts, are representing the company in two separate cases.
As well as the Sky-Virgin legal battle over carriage fees, Ashursts is also working with Virgin on its submission to a Competition Appeals Tribunal hearing into BSkyB's 17.9% stake in ITV.
BSkyB fears that material gathered by lawyers ahead of the Sky-Virgin case could be used against the satellite provider in the competition appeal.
Virgin Media is said to be concerned by Sky's reticence to release the documents for viewing.
Today's appeal is the latest in a long legal spat between the Murdoch TV provider and Virgin Media -- formed through the combination of NTL, Telewest and Virgin Media in 2006.
Virgin has accused Sky of anti-competitive behaviour and is suing the broadcaster, claiming that Sky ramped up the price charged to Virgin Media for its channels to be carried on the satellite platform.
Sky withdrew its basic package from Virgin last February after the companies failed to reach an agreement. The trial is expected in 2009.
Separately, Ofcom said yesterday it would include Sky's proposed subscription service on Freeview, named Picnic, in its investigation into the pay-TV market.
The regulator has published a number of consultation responses from the industry, including criticism from a number of Sky rivals about its position.