Many companies are expected to delay until next month a decision on whether to accept the controls - which could mean a sharp reduction in the rate of dividend increases - or go to the Monopolies and Mergers Commission.
There is, however, a growing feeling in the City that Offer will be more lenient than expected. Electricity shares ended last week on a strong note, hitting all-time peaks on Friday.
The Offer price cap applies to electricity distribution charges, which account for only one-quarter of household bills but make up the bulk of the companies' profits.
Professor Stephen Littlechild, Director-General of Electricity Supply, had been expected to tell the firms to cut prices by up to 20 per cent next April and to keep within a cap of inflation minus two or three percentage points.
But some analysts now suspect that the average one-off price cut could be no more than 15 per cent.
City analysts say that even on the less lenient price control formula the companies would still be able to increase dividends by between 4 and 6 per cent annually in real terms. They are nevertheless speculating that some companies may opt to go to the MMC.
The companies will receive little support from consumer groups. The National Consumer Council and the Consumers' Association are both calling for substantial cuts followed by a tight price cap.
They believe that shareholders have benefited disproportionately from privatisation and they hope that Professor Littlechild will significantly offset the introduction next April of the full impact of VAT on domestic fuel bills.
The Gas Consumers' Council has demanded government action to stop British Gas selectively increasing prices for many consumers as it prepares for competition in the domestic market in 1996.