The agency, one of the country's biggest quangos, also wants the right to oblige the companies to draw up contingency plans for droughts - which some of them have still not done. And it would like to impose financial penalties on firms which introduce drought orders, in the hope that this would concentrate their minds.
These proposals, which would require legislation, are being discussed with senior Department of the Environment officials and have been submitted to the House of Commons Select Committee on the Environment.
They reflect mounting anxiety about the threat to water supplies posed by recent dry weather, increasingly attributed to global warming.
The agency is particularly worried that profit-oriented privatised companies are ill-prepared to cope with a crisis, even after last year's Yorkshire Water drought fiasco.
High on the agency's list of concerns is transfers of water between companies. An agency report says: "Since the drought of 1976, the ability to make transfers has increased. However, the incentive to reach agreement to transfer water between companies is not the same as within a company's boundary, especially now that the water companies are privatised."
Under the new proposal, water companies with surplus water could be compelled to transfer it to neighbouring companies in need, despite any commercial reluctance they may have.
Geoff Mance, director of water management at the Environment Agency, said of the proposed new powers: "The object at the end of the day is to ensure that these issues don't slip off the list of management priorities and that the companies have no excuses left and no reason for senior managers not to address the issues."
The official concern about the effect of drought will be underlined by new evidence this week that action by water companies is threatening some of the most important environmental sites in England.
A report commissioned by English Nature, due to be published in the next few days, will show that the future of 56 sites of special scientific interest (SSIs) is at risk because too much water is being taken from surrounding areas.
In two- thirds of the most seriously affected sites, the report will show, the water authorities are the culprits.
The problems are caused by the abstraction of water from rivers or aquifers - a standard response to shortages of rainfall and low reservoirs. The effect is to lower the water table on the SSSIs, threatening their ecological balance.
"We need to make sure that steps are taken to protect these sites from any further damage," said English Nature's senior freshwater officer, David Witherington. "We feel there needs to be a national water resources strategy and that it needs to rely less on abstractions from rivers and aquifers during the summer and more on storage of winter rain."
Long-term planning of this kind is also a concern of the Environment Agency, which includes among its latest proposals a request for powers to insist that companies draw up plans to ensure that water supplies can be guaranteed far into the future.
Michael Meacher, Labour spokesman on environmental protection, yesterday gave his support to the idea of tighter regulation of the industry. He said: "This latest evidence [from English Nature] shows the short- sightedness of privatisation and the way it acts against the public interest. We have clearly got to reverse that. The Environment Agency is an obvious candidate for that role."