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After listening to protest speakers outside the University Union, the group of more than 40 chanting protesters left about 12.20pm and marched along George St footpaths until they reached Mr Woodhouse's office, south of the Exchange.
Organisers said members of the Young Labour and International Socialists student clubs and the Education Action Group had taken part in the protest.
Protest organiser and Young Labour president Ella Hardy said students had been "left out in the cold" by the National-led Government's Budget.
Finance Minister Bill English used the word "debt" many times in his Thursday Budget speech but did not mention the crippling burden of more than $10 billion of student debt, Ms Hardy said.
There was also concern about possible further student tuition fee rises, she said.
Police said protesters had been well behaved and the protest was without incident.