Members of the National Union of Rail, Maritime and Transport Workers (RMT), which represents about two-thirds of the network's 6000 staff, began a 24-hour stoppage at midday (1200 GMT) on New Year's Eve on Saturday.
London Underground bosses and Ken Livingstone, the British capital's mayor, have condemned the strikers as selfish for disrupting travel on a day when services operate all night to take revellers home from parties.
A Transport for London (TfL) spokesman told AFP that 22 of the network's 275 stations were shut at 4:30 pm (1630 GMT).
Among those closed was Covent Garden, an area of bars and clubs in the heart of central London's theatre district.
At King's Cross, the railway station serving Scotland and England's northeastern regions, two Underground lines were closed.
A TfL spokesman said: "So far the strike is having little impact on services. London Underground is still intending to run as full a service as it can, throughout the night. We expect to be able to provide service on all lines"
Trafalgar Square, usually the focus for London's mass gatherings, fireworks on the banks of the River Thames and the midnight chimes of Big Ben which signal the New Year are a traditional draw for thousands of Londoners.
London's party was set to kick off at five minutes to midnight with a massive fireworks display.
On Friday, Livingstone said the strike would "do nothing other than spoil a great night out for hundreds of thousands of Londoners".
London's party will kick off at
five minutes to midnight
The dispute is over the implications of a new 35-hour working week. The RMT agreed to the deal a year ago but is unhappy about new rosters, warning that they would compromise safety.
London Underground condemned the RMT's refusal to hold more talks to ward off the strike as "totally unreasonable."
However, the union insisted sentiment among its members was clear.
"We have balloted our 4000 members and they voted five to one in favour of the strike. Given the result of the ballot, we expect all of our 4000 staff not to go to work," spokesman Derek Kotz told AFP.
Police have warned party-goers, who may be tempted by the public transport strike to take their cars, not to risk drinking and driving.
However, any revellers affected by the strike can take some comfort in knowing that travel will be free on London's Underground, bus, tram and light railway services from 11:45 pm (2345 GMT) to 4:30 am (0430 GMT).