A similar campaign was aired earlier this month but was pulled after Virgin consulted its lawyers.
A statement issued by Sky said: "Should Virgin decide to ignore the wishes of their customers and drop the channels from 1 March, viewers are also told that they can join Sky."
It added: "The purpose of these communications is to appeal directly to cable customers and encourage NTL/Virgin to return to the negotiating table. Throughout these negotiations, Sky has consistently stressed that its priority is to ensure that cable viewers continue to have access to Sky's channels. The decision is in NTL/Virgin's hands and we urge them to commit to appropriate on-screen investment on behalf of its customers."
The satellite broadcaster has also said the the move would cost it £20 million in lost revenues rather than the £45 million claimed by Virgin Media.
Last week Virgin Media claimed that Sky had asked for double the fee to carry its basic channels which include Sky One and Sky News. Sky has since said that this was its starting offer and that it has now been reduced to a 30% increase.
Virgin Media responded by saying: "These promotions contradict Sky's claims that they want to negotiate with us and demonstrate what we suspected all along: that Sky has no intention of doing any deal."
Meanwhile, Virgin Media has announced a deal with ABC to air the first three series of Lost on its on-demand channel Virgin Central, with the third series available for viewing in August.