The draft bill, called the Investigatory Powers Bill will allow police to obtain warrants to examine the activity of people it or the other British security authorities.
But the warrants will have to be endorsed by specially trained judges.
The bill will also allow the authorities to hack peoples’ devices and to search vast amounts of data flowing through the internet.
GCHQ had already been doing this secretly, until whistleblower Edward Snowden revealed its activity.
Previous acts of Parliament had allowed councils to access data but they won’t be able to monitor internet data that service providers store.