Student complaints about universities have risen by a third in the last year and will rocket next year when tuition fees rise to up to £9,000, a watchdog has warned.

The Office of the Independent Adjudicator (OIA), which handles complaints from students at universities in England and Wales, said the near-trebling of fees would mean students will increasingly view themselves as consumers and be keener to insist on value for money.

For the first time this year, the watchdog has also named two universities – Southampton and Westminster – for breaking official rules on how to handle students' complaints.

From autumn 2012, universities will be allowed to charge tuition fees of up to £9,000 a year – up from £3,375 this year. Students will only pay the fees when they have graduated and are earning £21,000 a year or more.

The OIA's annual report, published on Tuesday, shows that the number of complaints made by students has risen by a third in the last year to 1,341 (0.05% of students). The watchdog said the actual number was likely to be seven times this because the OIA only deals with cases in which a student has exhausted their university's complaints procedures.

In the last two years, the number of complaints dealt with by the watchdog has doubled. This year, a fifth of complaints were partially or fully upheld.

Rob Behrens, chief executive of the OIA, said he would "not be surprised" if the number of complaints rose by a third again once higher fees had been introduced.

Students were more likely to complain in future because of higher tuition fees, greater information on university websites and greater competition for graduate jobs, he said.

The government has told universities they must publish by September next year how much contact time students can expect from their lecturers in each of their courses. Ministers are also urging universities to issue student charters, setting out students' and institutions' rights and responsibilities. Fierce competition for jobs means students are more likely to complain if they are awarded poor marks in exams or coursework.

"There will be more transparency, so students will be better informed about their rights," Behrens said. "The tuition fee rise will come in, and so students will be more aware of their entitlements because of this, and at the same time the labour market may not get any better."

The OIA's annual report shows the students most likely to complain are those who pay the most. Some 29% of complaints in the last year came from students whose home country is not the UK. In England, 16% of students are from outside the UK.

The watchdog said the universities of Southampton and Westminster had failed to comply with formal decisions made by the OIA. Westminster mishandled two complaints. One was from a student who argued that their disability had not been properly taken into account, while another student claimed an exam question and its marking scheme had been unreasonable. The university had failed to resolve the cases fully and promptly, the OIA said.

Southampton continued to oppose the watchdog's conclusion that an undergraduate had a legitimate complaint about a placement and deserved compensation. It failed to comply with the OIA on another case, and delayed the investigation of another by 10 months.

The majority of complaints are from students who take issue with their exam or coursework marks, the watchdog said. In the last year, the OIA awarded £173,959, with £15,000 the biggest single payout. The previous year, a total of £163,343 was awarded.

• How well do universities deal with complaints? Education Guardian, page 6