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
The largest advertising firm in the world and a global law company with offices in London were among the targets.
The Queen, Duke of Edinburgh and other members of the Royal Family have attended the funeral of Countess Mountbatten of Burma.
Shop owner Jel Singh Nagra changed the name of his North Tyneside store after threat of legal action from Sainsbury's