He spoke after John Major and Ms Latimer, a caterer, refused to accept the statement of regret published in this week's New Statesman, which last week detailed rumours linking their names.
Mr Major's solicitors, Biddle and Co, said he was not satisfied and the action would continue 'until the New Statesman and the other defendants take a realistic view of the matter'.
Ms Latimer's solicitors, Swepstone Walsh, spelled out their demands more clearly, saying: 'We want a full apology and we expect to be properly compensated.'
Mr Coyne said: 'They seem to be on a treasure hunt. It's Maxwellian, the way they're going about it.' The late Robert Maxwell was notorious for his many libel actions.
Earlier John Menzies, one of the two wholesalers who distribute the New Statesman, refused to handle this week's edition. It means a loss of 3,600 copies, or about 15 per cent of its circulation.
The letter sent to Biddle's by the New Statesman's solicitors, Bindman and Partners, was printed over a full page in yesterday's issue of the magazine. It said the offending article had not meant to suggest any improper relationship between Mr Major and Ms Latimer.
Mr Major and Ms Latimer are also continuing their actions against the magazine's printers, BPCC, its distributors, Comag, and its two wholesalers, John Menzies and W H Smith, as well as against Scallywag, the fringe magazine that first published the rumours.
W H Smith wrote to the plaintiffs' solicitors yesterday responding to their original complaint. The letter said that it would be impossible for the company to read every magazine it handles before putting it on sale, and that within an hour of being informed of the legal action copies had been withdrawn from sale.
The New Statesman indemnifies its distributors and printers against such legal actions, but the indemnity would be worthless if the magazine were to be bankrupted by its own legal costs.
John Menzies would not say last night why it would not distribute this week's issue. Mr Coyne said: 'The best way they can make sure we won't be able to pay is by not distributing us.'Reuse content