Members of the Rail, Maritime and Transport (RMT) union working on the Hammersmith & City and Circle lines walked out at 21:30 BST.
The strike comes amid claims that industrial relations have broken down.
Transport for London (TfL) had warned there would be no Hammersmith & City line service and a limited service on the Circle line from around 21:00 BST and throughout Friday.
The RMT has accused TfL managers of being "heavy handed", including putting staff toilet breaks on a stopwatch and a "flagrant disregard" for agreed policies and procedures.
RMT general secretary Mick Cash said: "This dispute is about the basic issues of protecting working conditions of our members and defending agreements from attempts to drive a coach and horses through them."
Operations director Steve White said London Underground understands drivers need to take a break but said "a minority are taking breaks of an hour or more and calling them toilet breaks," which had a direct impact on customers.
He said it as "absolutely not true" toilet breaks were being timed, but said management was offering help through an occupational health team if a driver has issues requiring longer breaks.
TfL has advised commuters to check its website for travel information, but said all other TfL services would be operating as usual.
Tube drivers on two London Underground lines have begun a 24-hour strike.