LONDON (Reuters) - Prime Minister David Cameron came under growing pressure on Sunday to halt Rupert Murdoch's bid for pay-TV operator BSkyB, at least until an investigation into phone-hacking at the media magnate's newspapers has been completed.

Opposition leader Ed Miliband said he would force the issue to a parliamentary vote this week if Cameron failed to act.

"I hope he changes his position on this. I don't want to have to force a vote."

Pressure came too from members of the government's junior coalition partner, the Liberal Democrats, who have traditionally had a less cozy relationship with Murdoch.

Deputy LibDem leader Simon Hughes said he would be prepared to back Labour's call for the deal to be postponed and urged other LibDems to do the same -- setting the stage for a major test of the coalition's unity.

Murdoch's News Corp <NWSA.O>, the world's largest news conglomerate, has made a $14 billion bid for the 61 percent of the profitable pay-TV operator BSkyB <BSY.L> that it does not already own.

Murdoch was flying into London on Sunday to try to save the deal after a phone-hacking scandal caused a public outcry and forced him to close the News of the World, the first British paper he bought in 1969.

Cameron has ordered a judge-led enquiry into the phone-hacking allegations but has so far resisted calls to end Murdoch's attempt to buy out BSkyB.

Transport Secretary Philip Hammond said he understood public concern over an expansion of Murdoch's empire but the government had to operate within the law.

"The government can't just change the rules in mid-stream. If we did we'd undoubtedly be taken to court and we'd probably lose," he told Sky News.

But the phone-hacking allegations have prompted Britain's media regulator Ofcom to say it will consider whether News Corp directors are "fit and proper" persons to run BSkyB.

Shares in BSkyB shed more than 7 percent on Friday on growing doubts that the deal would go through.

(Reporting by Christina Fincher, editing by Tim Pearce)