LONDON (Reuters) - British lawmakers passed on Tuesday a new surveillance law to give security agencies more extensive monitoring capabilities in the digital age after several amendments were added to better protect privacy.

Lawmakers voted 444-69 in favor of the Investigatory Powers Bill, which interior minister Theresa May said would help "keep us safe in an uncertain world". The bill will now go to the House of Lords upper house of parliament.

Several lawmakers, including the opposition Scottish National Party, voted against the bill, saying that the protections for privacy were not strong enough.

Last November, Prime Minister David Cameron's government announced plans for sweeping new powers which would force tech firms to store details of every website people visited for a year as well as spelling out the ability of spies to collect bulk data and hack into individuals' computers and smartphones.

Calling the scrutiny of the bill "unprecedented", May said there was a new privacy clause that would require agencies to consider less intrusive means to achieve the same ends and special protections for lawmakers, lawyers and journalists.

"It provides far greater transparency, overhauled safeguards and adds protections for privacy and introduces a new and world-leading oversight regime," May told parliament.

A debate about how to protect privacy while giving agencies the powers they need has raged since former U.S. intelligence contractor Edward Snowden leaked details about mass surveillance by British and U.S spies in 2013.

(Reporting by Elizabeth Piper; editing by William Schomberg)