A petition asking the UK government to repeal its new Investigatory Powers Act now has more than 118,000 signatures.
This means that it must now be considered for parliamentary debate.
Internet providers will soon have to record which services, external their customers' devices connect to - including websites and messaging apps.
They must keep this information for one year and share it with various departments and organisations on demand.
The government says it will help in the fight against terrorism.
Its critics have named it the "snoopers' charter", and it is described in the petition, external as "an absolute disgrace to both privacy and freedom".
The act was first proposed by Prime Minister Theresa May when she was Home Secretary and was approved by the House of Lords on 19 November.
It is expected to become law by the end of 2016.
Blogger Chris Yiu compiled a list of the 48 organisations and departments, external that will be able to access the browsing records of individuals without a warrant.
They include various police, military, government and NHS departments as well as the Food Standards Agency, the Gambling Commission, the Financial Conduct Authority and the Health and Safety Executive.
The required data, external covers only the domain name of each site visited - www.facebook.com or www.bbc.com, for example - not the individual pages within them.
"So long right to privacy, hello 1984," wrote Mr Yiu.