Mr Anderson called the EGM after falling out with the management, and he tabled a motion seeking the replacement of the company's chief executive, David Oertle, and the removal of its two lead venture capital backers from the board.
Warburg Pincus and Apax Partners, one of Europe's largest venture capital funds, support Mr Oertle, and in a counter-motion are seeking to strip Mr Anderson of his directorship, despite his control of 27 per cent of the company's shares.
The vote on the tit-for-tat motions hinges on the decisions of two large US institutional investors, according to observers - Fidelity and the College Retirement Equities Fund - and Mr Anderson conceded on Friday: "Fidelity is not voting with me."
Discussing the possibility of being ousted from the company he helped to found in 1992 as "a European MCI", Mr Anderson vowed to fight on. "I can mount a proxy fight at the annual general meeting in March," he said.
"Or I can make a tender offer for the company. My track record with the investment banking community is excellent. Or I can set up a new company to compete against Esprit." He said many of the company's 700 employees remained loyal to him.
A spokesman for Esprit expressed scepticism about Mr Anderson's plans. "It would take $1bn (pounds 600m) to buy Esprit," he said. "Can he raise that?"
Esprit sells national and international long-distance services to companies in Britain, the Netherlands, Spain, France, Germany, Belgium, Italy and Ireland. On Friday, it announced a pre-tax profit of pounds 17.1m on turnover of pounds 82.6m for the year ending 30 September, up 55 and 82 per cent respectively over 1997 results.
Sir Robin Biggam, who joined the company as non-executive chairman in October, said the results "confirm that the strategic direction in which the company is moving is the right one, and that the right senior management is in place".
The company has a relatively low profile in the City because its shares - about 30 per cent of which are held by independent investors - trade on the Nasdaq and Easdaq over-the-counter exchange rather than the London Stock Exchange. But within the telecoms world, the no-holds-barred nature of the battle between Mr Anderson and Esprit's management and venture capital backers has rivals mesmerised.
Esprit portrays the battle in terms of a brilliant but mercurial entrepreneur outliving his usefulness. Mr Anderson portrays it in terms of boardroom skulduggery. He says that if the situation is not resolved in his favour by the March AGM, he will abandon his struggle.Reuse content