The pattern of ownership and control of British industry is unusual compared with most other countries in that ownership is relatively dispersed. Typically the largest shareholder in any large listed company is likely to own a voting minority of the shares. Majority ownership by a single shareholder is unusual. It is not uncommon for the largest shareholding to be under 20 percent and in many cases it is much less than that. A broadly similar pattern is observed in the USA. Two inferences about corporate governance are conventionally drawn from this, following the early work of Berle and Means: (1) All but the very largest shareholders are typically too small to have any real incentive to participate in decision making; (2) All but the very largest shareholdings are too small to have any real voting power. The question of voting power is the focus of this paper. Conventional analyses use a rule of thumb of 20%, assuming shareholders to be fundamentally passive in relation to the running of the company, whatever their style of investment management, unless one of them is above this figure. The London Stock Exchange defines a controlling holding to be one greater than 30 percent. Much empirical work uses declarable stakes, which in the UK are those of 3 percent or more, and disregards anything smaller assuming it to be powerless. In fact, however, a 1% stake in the 100th largest company (Smiths Industries) is worth about £29million, which suggests its owner has strong incentives to be active, and might wish to use his voting power. Theoretical voting power of minority shareholding blocks is studied using the gametheoretic idea of voting power indices. This is applied to a model of ownership control based on the definition of control used by Berle and Means in their classic study. The results give support for use of a 20 percent rule in many cases but not all. Also they support the idea that many companies are potentially controlled by a block of a few large shareholders working in concert.