In an interview with The Sunday Telegraph the London Mayor hit out at Mr Cameron's call for the European Central Bank to deploy a "big bazooka" - effectively printing money - to help bail out the stricken economies in the south of the continent.
Mr Johnson also attacked plans, backed by the British government, for the 17 eurozone countries to share closer fiscal links, making them more unified on tax and spending.
"What I don't think you can do, is just pretend that you can create an economic government of Europe, effectively run by Germany," the Mayor added.
He described the replacement of elected leaders in Greece and Italy with governments led by technocrats as "completely mad" and warned that if the rest of the EU went ahead with a plan to impose a "Tobin" tax on financial transaction, even without British participation, it would be seen as a "hostile act" because it would still hit so many deals in the City of London.
Mr Johnson also outlined his own "orderly" solution to the crisis - which was miles away from anything suggested by any member of the British government.