The proposed measures, which were unveiled in November, would allow security agencies to access the Internet communication records of suspects and require web and phone companies to keep records of all activity for 12 months, among other measures.
The "draft Investigatory Powers bill could, if adopted in its present form, threaten the rights to freedoms of expression and association both inside and outside the country," the experts said.
Among matters of concerns were the "excessively broad definitions and disproportionate procedures to authorise surveillance, including mass surveillance, and data retention without adequate independent oversight and transparency."
The group of three UN special rapporteurs, David Kaye who deals with freedom of expression, Maina Kiai, who specialises in freedom of peaceful assembly and Michel Forst, an expert on human rights defenders, called for "a comprehensive review" of the bill "to ensure its compliance with international human rights law."
Other rights groups have condemned the draft bill as an attack on civil liberties, while technology giant Apple has said that complying with it could pose significant problems.
Critics have focused in part on measures that would allow the security agencies to "interfere" with personal devices to obtain data.
Home Secretary Theresa May has said the bill would make existing surveillance laws more transparent and update them to take into account the growth of online communications.
The bill would also install a new way for approving warrants for data interception, making a judge's authorisation mandatory.
May has said this measure should allay fears of excessive government intrusion.