Broadband users should not be disconnected for downloading music and films illegally, according to the police and intelligence services.
Organisations including the Serious and Organised Crime Agency and the Metropolitan Police are believed to be against the government's plans, which would see the web accounts of persistent offenders suspended.
According to the Times, such a move is likely to push pirates to consider ways to avoid detection, which in turn could prove problematic.
Talking to the newspaper, an insider said: "It will make prosecution harder because it increases the workload significantly."
In addition, the source added that bodies including MI5 are not keen on the concept, stating: "They think it is only going to make monitoring more difficult."
News of opposition to the plans has come after French broadband provider Vivendi called on its UK counterparts to support efforts to tackle the issue.
A "three-strikes" law was recently launched in France.