Lord McAlpine's lawyer said ITV should pay "a little bit more" compensation than the BBC over false claims linking the peer to child abuse because its infringement seemed to be "premeditated".
Andrew Reid told Channel 4 News, "They [ITV] don't quite see their transgression as being as serious as that of the BBC, whereas our advisors see it as being far worse, particularly because it looks as if it was premeditated".
Following comedian Alan Davies' apology to Lord McAlpine earlier this evening, Mr Reid said, "I'm surprised he hasn't apologised a lot earlier bearing in mind the huge amount of tweets".
Mr Reid said Twitter users with a large number of followers - such as Sally Bercow and Mr Davies - will be receiving letters before any legal action is taken.
More top news
Hungarian Prime Minister Viktor Orban is to meet with European Union leaders in Brussels today to discuss the migration crisis.
Drinkers subsidise non-drinkers by £6.5 billion a year, a report claims.
Tight security in Beijing as China marks the 70th anniversary of the end of World War Two with a huge military parade.