Steve Grant of the drivers' union Aslef told the BBC, "It's been 100 percent solid from our members."
The union was demanding triple pay and a day off for working on Sunday.
London Mayor Boris Johnson said, "The demands being made by the leadership of Aslef are monstrous. It has been clear ever since the Gregorian calendar was reformed in the mid-18th century that Boxing Day 2010 would fall on a Sunday. So why do they demand more money with three weeks to go?"
London Underground said it would run as many trains as possible, along with 700 bus routes and some river runs.
The railroad's managing director, Mike Brown, said: "The union leadership has shown complete disdain for all who want to visit family and friends or hunt a good bargain during what is one of the busiest shopping days of the year."
In 1996, Aslef agreed to consider Boxing Day a normal working day in return for higher pay and longer holidays. But it said increased service on bank holidays meant drivers now had to work more holidays.