The bin lorry was doing its rounds in Lumber Lane, Worsley, when a resident captured the prominently positioned leaflet on camera.
Ben Cardwell, 24, who lives with fiancee Louise Morris, 29, said: "It took me totally by surprise. I was shocked by it. I called my fiancee to have a look and we both couldn't believe it.
"I wanted to put a complaint to the council. We didn't think it was allowed to put stickers up supporting any political party, never mind the BNP."
The council say investigations are continuing, but union bosses say the staff responsible should be suspended with immediate effect.
Alec McFadden, of Salford Unison, said: "I have never known any public authority to allow support of any political party, whether that be Labour or the Conservatives.
"It makes it ten times worse that it is the BNP - a fascist, racist organisation.
"The council should be taking immediate action and should suspend whoever is involved as soon as possible.
"The investigation should take place to find out who is involved but the council should be seen to respond quickly. This is a very serious matter."
Salford council has confirmed formal action will be taken against whoever put the flyer on the wagon, but has stressed it is still investigating the claims.
Coun Joe Murphy said: "The council has clear rules against using council property to promote political parties in this way.
"I've asked for a full investigation and formal action will be taken. However, until the investigation has been completed it's not appropriate to comment any further."
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umpire 2, Salford M7 4HT (15/07/2009 at 12:28)
Recently we had two persons who were involved in gun crimes, jailed and then should be deported back to their own country but they have appealed because they are worried over how they will be treated when they get.
Instead this country is deporting families who have put something back into society, working, paying taxes, etc.....
It is time to get real.....with what is actually happening in the UK