But the report said the unified service failed to offer value for money, because of long and numerous delays to tuition fee loans and maintenance grants.
The report said the firm underestimated the task it was taking on and was not properly prepared.
It made slow progress, with only 46% of the applications fully processed by the start of the 2009 term compared with 63% the previous year, it added.
Overall, it processed claims a third more slowly than local authorities had the previous year.
It had used a new document scanning system which was untested and then failed.
This led to a dramatic increase in the volume of telephone calls, with the company receiving four million in September alone - 87% of which went unanswered, the report added.
Antonia Johansen, student: "I had to borrow a lot of money."
Over the 12 months from February 2009, it only answered about half of the telephone calls made to its call centre.
Thus, customer service was "poor", the report said, with half of students surveyed by the NAO saying they had been asked to send the same paperwork more than once.
"As paper evidence arrived, the company failed to store it in a way that was easy to retrieve and a backlog built up," the NAO said.
But the firm's board was "not aware of the difficulties with processing applications until it was too late to prevent major problems", it added.
The report concluded: "The company expects to process at least twice as many applications in 2010, when it becomes responsible for applications from both first and second years, and it is unproven whether it has the capacity to provide a good service this year."
Angela Harrison, BBC News Education Reporter
This is the second but most hard-hitting of the two published reports into the problems at the Student Loans Company.
As well as using tougher language, the National Audit Office has exposed just how bad the delays were.
In September, as students and their families bombarded the SLC with phone calls - most of which went unanswered - the SLC admitted to "telephone problems" only, not to delays or technical problems.
The inbox of BBC's News website's education team told a different story - of long delays and missing documents as well as financial hardship.
Bosses promised that those who had applied on time would be paid on time. That did not happen. Everyone is hoping these latest pledges can be kept.
It added: "Avoiding a recurrence of the 2009 problems is of the highest priority for 2010, but substantial risks remain to successful delivery of the service."
The SLC says it has made several significant changes, including increasing the number of people who take calls and improving training.
Speaking on the Today programme on BBC Radio Four, its chief executive Ralph Seymour-Jackson said: "I am really sorry for the problems and delays and difficulty people had in getting through to us last summer.
"We didn't give them the service they have every right to expect. Lessons have been learned. We've put right the problems of the past and we will make sure they get the right service this summer."
And he made this pledge: "I can say if the student gets me their application with all the evidence by the key deadline of the end of June, I will make sure they have their money by the start of term when they register at university."
The Department for Business, Innovation and Skills also came under fire from the NAO, which said it had failed to monitor the firm properly.
It said "weaknesses" in the SLC identified in 2006, should have "served as a warning of the risks attached to such a challenging programme".
Ralph Seymour-Jackson, Student Loans Company: "We've put right the problems"
Higher Education Minister David Lammy said PricewaterhouseCoopers LLP would carry out an independent check that the SLC was ready to process applications and answer customer enquiries during the peak summer months.
And an extra £16m would be ploughed into the firm to bolster its operations.
He said: "It is clear that the service offered by the Student Loans Company last summer fell well short of expectations.
"It is important that we can be confident students and their families receive the service they deserve from the SLC throughout the rest of this year."
National Union of Students president Wes Streeting said students would feel "sick to their stomachs" at the prospect of a repeat of last year's delays.
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