Rival proposals will be considered by the Privy Council on October 9, and The Independent's Chris Blackhurst said it would be hard to "ignore what's been going on".
Mr Miliband insisted his dispute over the Daily Mail's claim that his father "hated Britain" was not about regulation but "responsibility and right and wrong".
Mr Blackhurst said he hoped the row would not influence the Privy Council but accepted it had "driven a wedge between politicians and the press".
Hesaid in a radio interview: "The truth is we are all human and it's very hard for people sitting round that table next week to ignore what's been going on.
"I certainly think it will have driven a wedge between politicians and the press. I hope they don't really consider it, we are only really talking about one article this week... the whole of press regulation should not hang on one article."
Following the Leveson Inquiry the newspaper industry rejected the idea of "state-sponsored regulation" and put forward a rival plan, which is being examined by a sub-committee of the Privy Council.
Mr Blackhurst, group content director for The Independent and Evening Standard, said he expected the industry's proposals to be rejected.