The CPS has discontinued the case to allow the Manchester police more time to look into the circumstances surrounding the alleged theft of documents connected with Mr Regan's plans to launch a bid for the supermarkets to funeral parlours group earlier this year.
The deal collapsed after one of the main financial backers of Galileo, the takeover vehicle set up to make the bid, pulled out. The decision to drop proceedings will not prejudice the CPS's ability to take further action against Mr Regan.
Shares in Lanica Trust, the investment vehicle run by Mr Regan, are likely to stay suspended while the question marks surrounding the bid remain. The shares were suspended on 10 February.
A spokeswoman for the London Stock Exchange said there had been no approach from the company to lift the suspension following yesterday's development. Depending on the Greater Manchester police's findings, the CPS may decide to restart proceedings against the 31 year-old Mr Regan. It may, however, decide no further action is warranted.
A spokeswoman for CWS said that yesterday's move was intended to facilitate the investigation and represented a "suspension of the proceedings rather than their conclusion".
"As this is a matter for the authorities and is out of our hands it would be inappropriate for us to comment further," she added.
The CPS took over CWS's private prosecution at the end of June. Former Co-op executive Allan Green had been charged with the theft of confidential Co-op information and Mr Regan and his partner David Lyons with aiding and abetting.
The decision to drop the current case was taken after police advised that the complexity of the case was likely to require more time. That investigation is now expected to take a number of months.The CWS affair has already claimed victims. Three bankers at Mr Regan's advisers Hambros resigned in July after an investigation said their conduct had fallen "well short of the standards of good business practice".