After agreeing libel settements of £185,000 and £125,000 respectively with the BBC and ITV, lawyers for Lord McAlpine are now set to focus on "high-profile" Twitter users.
Solicitor Andrew Reid told ITV news that these individuals, who include journalists, are to be asked to pay damages running into the thousands.
The ITV settlement stemmed from a decision by This Morning presenter Phillip Schofield to research a list of alleged Tory paedophiles from the internet and then show the list to Prime Minister David Cameron. Names on the list were briefly visible on camera.
Reid told ITV: "This was a sensible settlement. We accepted ITV’s position that the fire was well lit by Newsnight and the stunt that Mr Schofield pulled really just added oil to the flames."
Asked whether the "big Twitter users" will get away with an apology and a donation to Children in Need, Reid said: "No. I don’t think they will be, no… I think most importantly we get an apology and an undertaking not to repeat and once we’ve examined the extent of the damage they’ve done, we’ll agree suitable damages."
He agreed that those damages would be in the thousands and asked about the number of individuas involved he said: "There are a large amount but at this stage we’re looking at twenty."
Asked if they are people who have come forward, Reid said: "Well they haven’t come forward to us. Some of them we’re aware of, some of them have come forward and some have been very apologetic. You know all of this will be borne in mind, in the same way that ITV were apologetic, as were the BBC."
He added: "I think the government having seen this will need possibly to have a clear piece of legislation to make sure that Twitter can't be used to bully…it’s all social media. People who have been coming to us didn’t realise the impact of these tweets."