The surprise set was held in an abandoned bank owned by the Swiss company UBS as a thank-you to the protesters for their part in the global movement for social and economic justice.
The Occupy London movement organised an alternative Christmas party featuring a collection of poets, dancers and comedians in the basement of the Bank of Ideas building on Sun Street.
The event coincided with the actual UBS Christmas party, which took place just down the road.
The performances have been recorded for an album and HD video, which will be available for fans to buy and help raise money for the occupation.
Adam Fitzmaurice, an Occupy London supporter who helped to arrange the event, said: "Thom Yorke, 3D and Tim Goldsworthy wanted to do something to show their solidarity and say a big thank-you to Occupy London and the Occupy movement around the world.
"Their intervention is an important cultural response to the economic injustice that is happening and will hopefully help ensure that more people join the fight.
"This is just the beginning: we've a raft of live performances in store, so now is the time to be involved!"
The Occupy London movement has announced that December 15 - which marks two months since the start of the protest - will be named Occupy Everywhere and has called for a UK national day of action.
> OccupyLSX protesters 'expose media' over empty tent claims - video