Vodafone’s strategy in the US has bedevilled Arun Sarin, the group’s head, since he became chief executive in 2003.

In 2004 his frustration with Vodafone’s Verizon Wireless holding triggered an ill-judged and unsuccessful bid for AT&T Wireless, as Vodafone sought to secure 100 per cent control of a US group.

The performance of Verizon Wireless, in which Vodafone has a 45 per cent stake, is not at issue — though its dividend policy is.

In the 2006-2007 financial year alone, the carrier enjoyed a 15 per cent increase in its customer base to 62 million, and a 17 per cent increase in its revenues.

Analysts’ estimates now put a value on Vodafone’s holding in the business of $54 billion (£26 billion), up from $38 billion a year ago.

The problem, say critics, including ECS, is that the true worth of that stake, which contributes to well over 20 per cent of Vodafone’s underlying operating profit, is not reflected in Vodafone’s share price.

In addition Verizon is not paying out any money — it stopped issuing dividends two years ago — and Vodafone has no control over that.

The financial engineering suggested by ECS to “unlock” the value in the holding met with short shrift from Vodafone, and yesterday investors also indicated they have no confidence in such complex proposals as an independently listed Verizon tracker stock.

Instead, most analysts believe that the most effective way to unlock value from the holding is for Vodafone to exercise its “put” option and simply sell the stake back to Verizon’s parent company, Verizon Communications.

To date, Vodafone has argued that this would generate a punitive tax bill, but that might not placate the City for ever.

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