Mr Campbell served as Mr Blair’s director of communications and was seen as one of the key figures associated with the New Labour project.
However, Mr Campbell said the SNP was behaving as if “owns every part of the country” as he compared the attitude of Nicola Sturgeon’s party to that of New Labour towards the end of its years of dominance, including when the party was ousted from power at Holyrood in 2007.
Speaking during a campaign visit to support Labour frontbencher Ken Macintosh’s bid to be re-elected, as the Eastwood MSP, Mr Campbell said: “The Scottish Labour Party allowed itself to get very complacent and became seen to be very arrogant.
“We’re seeing the same stuff from the SNP with a taking people for granted.”
Mr Campbell, in a speech to Labour supporters in Eastwood, also said that there was an “aura” around Ms Sturgeon and the SNP, but stated “that’s all it is”.
He added: “When you see Nicola Sturgeon, you can’t say she anything, but popular, but it’s like she’s floating above politics and that’s unreal.
“It’s spin and they are brilliant at it.
“There is this mood music and this aura around the SNP and Sturgeon in particular. But that’s all it is.
Mr Campbell also said the SNP has brought homelessness back to Scotland and that he was “shocked” by the number of people he saw sleeping on the streets in Edinburgh and Glasgow.
In a fierce attack on the SNP’s claim to be a party of the left he said homelessness in Scotland’s main cities is as bad in parts of London.
He said: “I came here recently and I was shocked by how many people I saw sleeping on the streets, particularly in Edinburgh and Glasgow.
“A progressive government doesn’t have that.
“We had a massive problem with rough sleeping, but the Labour government made that a thing of the past.
“But now that’s back in England and it is in Scotland too. How can you call yourself a progressive government if that’s there and you do nothing about it.”
An SNP spokesman, hitting back, said: “Alastair Campbell was one of the key architects of Blairism, which has left a toxic legacy that Scottish Labour are still unable to shake off.
“The SNP has a record to be proud of – with more young people in work, education or training than ever before, crime at a 41 year low and some of the very best quality healthcare to be found anywhere in the world.
“We go into May’s election asking for voters in Scotland to back Nicola Sturgeon and the SNP on that record and our vision to keep Scotland moving forward.”