Observers said rival telecoms operators such as Sprint, the US giant, could take the chance to make an approach.
Shares in C&W fell 30p to 695p on the day as investors mulled over the 51-year-old Texan's surprise resignation. He is leaving to be chairman and chief executive of EDS, the troubled US computer services giant.
Mr Brown will be replaced by Rod Olsen, a long-serving C&W executive who had been due to retire by April 1999, until a permanent successor is found in the new year.
Although Mr Brown is credited with shaking up C&W during his 29-month tenure, the company still faces big strategic challenges. A proposed alliance with Telecom Italia recently fell through, prompting C&W to go it alone in continental Europe. It still has no partner in the key US market.
Mr Brown is understood to have offered his resignation to Sir Ralph Robins, C&W's chairman, on Wednesday evening, before informing other directors on Thursday.
Former colleagues yesterday said Mr Brown had been attracted by the massive compensation package he is likely to receive at EDS, while he also wanted to return to the US for the sake of his family.
As chief executive, Mr Brown executed a flurry of deals, including the consolidation of the UK cable industry into Cable & Wireless Communications and buying MCI's worldwide Internet business.
"He was ruthless and very self-centred," one C&W executive said yesterday. "But he did have decision-making capability. What he's done is put spirit into the company."Reuse content