Murdoch's previous attempt to buy Sky through his News Corp business provoked uproar among some UK politicians, who said it would give the billionaire owner of The Sun and The Times newspapers too much control over the country's media.
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The latest proposed deal would give Fox control of a pay-TV network spanning 22 million households in Britain, Ireland, Austria, Germany and Italy.
"We're aware of the proposed merger," May's spokeswoman told reporters. "It is not something it would be appropriate for government to comment on."
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