The Communication Workers Union (CWU) said it will target the headquarters of UBS, Goldman Sachs and Merrill Lynch during a bus tour across London.
Protests will also be held outside the Business Department, Ofcom and offices of the Conservative and Liberal Democrat parties, while a giant postcard opposing privatisation will be delivered to the Royal Mail.
Billy Hayes, CWU general secretary, said: "Royal Mail is thriving in public ownership, increasing its profits, providing good quality services and decent jobs. We want it to remain that way. Privatisation would be a throwback to the tired old politics of the 1980s.
"This week of action will take the uncomfortable truth to the doors of those who are working on flogging this national asset. Privatisation is unpopular, unnecessary and will be fought by a tide of growing opposition."
Politicians from Labour, SNP, Plaid Cymru, Green and SDLP parties took part in a packed meeting in Westminster last week amid growing warnings about the impact on jobs and services if the sell-off goes ahead.