During a debate over the Digital Economy Bill this week, members of the parliament said copyright holders are trying to push the law too quickly.
The debate centred on the "three-strikes rule" which would suspend the internet connection of anyone accused three times of copyright infringement. Such a rule could affect organisations such as libraries, internet cafes and universities which offer free internet access.
Conservative politician Lord Young said that organisations should take adequate measures to prevent illegal activity.
The reading of the bill will continue this week.