Harriet Harman's appeal for cross-party talks on media monopolies fell on deaf ears in the Commons this morning, as the culture secretary rejected the need for "further political discussion".
Labour wants to continue the trend of cross-party negotiations begun in the deal struck over media regulation following the conclusion of Lord Justice Leveson's inquiry last autumn.
His final report acknowledged it had not been forced to neglect media plurality issues, leaving Labour backbencher Katy Clark to raise the issue in culture, media and sport questions this morning.
"Media and newspaper ownership is too concentrated in the hands of too few," she told MPs.
"There is a need for a cap in the different sectors of the media on ownership."
Miller rejected that approach - and agreed with Tory backbencher Andrew Bridgen when he said "any regime must strike the right balance between plurality and allowing growth in the industry".
The culture secretary replied: "We don't want to have a situation where companies would not want to invest in the UK for fear of running into an unnecessary cap on their expansion."
The Department for Culture, Media and Sport is holding a consultation on the issue this summer, but Harman used her contribution to the session to suggest a repeat of the cross-party negotiations might be a better approach.
"Media ownership prevents the market operating by preventing new entrants to the market, as well as being bad for democracy," she said.
"I'm sure the Liberal Democrats and certainly we would be very willing to work to support this part of the Leveson inquiry, which is important and has not yet been tackled."
Miller replied: "I think we already have an agreed way forward on this, which is we're going to be seeking views on this in the summer.
"As Leveson himself said, he wasn't able to devote sufficient time to look at media plurality matters in detail.
"That's what we need to do now, so rather than having further political discussion on this I think we need to seek views on these issues to provide the broad policy framework we need in this area."
The government's submission to the Leveson inquiry on media ownership issues insisted that any rules act as a "potential constraint" on the market, "so it is essential that they be proportionate and do not unnecessarily restrict growth and innovation".
Then media secretary Jeremy Hunt removed local ownership rules to enable partnerships between local papers, radio and Channel 3 television stations in 2011.
But a number of rules continue to be in place. No one can own more than 20% of a Channel 3 licence and national newspapers with more than 20% of market share.
Political parties are prohibited from holding any broadcasting licences.
The secretary of state also holds the ability to implement a media plurality public interest test, enabling him to intervene in media mergers where he or she has concerns about media plurality.
Harman has called for a media ownership cap as low as 15%. She used her speech to the annual Charles Wheeler lecture on journalism last week to outline detailed proposals about how such restrictions could operate.
"Limits and thresholds do not always have to mean divestment," she said.
"We favour clear bright lines – a top line limit which could trigger divestment, but also a bottom line, with a regime of obligations (which might include editorial independence, independent governance and promoting plurality in other ways) in between. At the Leveson inquiry, we suggested a 30% top line and a 20% bottom line for newspaper ownership, but we all need to think about where the limits are drawn.
"The process should also decide on a robust 'fit and proper person' test. It should be extended to cover impropriety and failures of good governance, and allow for interventions in a merger on propriety as well as plurality grounds."