Far from being irresponsible Covid spreaders, the vast majority of students at English universities have been vaccinated at least once and would request a test if they had symptoms, according to a survey.

Students’ wellbeing has suffered this autumn, however, with a third of those surveyed reporting that their mental health had deteriorated since the start of term, the report by the Office for National Statistics (ONS) says.

The survey found the average life satisfaction score among students was 6.6 out of 10, significantly lower than among 16- to 29-year-olds in general, who scored 7.0, and the overall adult population in Great Britain, at 7.1.

The ONS report says mental health has worsened as the term has progressed, with 32% of students reporting that their wellbeing has deteriorated, compared with 26% in late September.

It is better than it was last May, when half of students who took part in the survey said their mental health had deteriorated. Most students at that time were studying online owing to lockdown restrictions, while this term students have returned to campuses for more face-to-face teaching.

On vaccination, the survey – which is based on experimental data drawn from responses from almost 1,000 students in England during October and November – found that 91% of respondents had been vaccinated against Covid at least once.

The proportion of students who have been double-vaccinated was 85%, up from 78% in late September. Of the 8% who said they had not been vaccinated, almost a third (32%) said they were fairly or very likely to take a vaccine if offered.

Students also showed they were willing to test for Covid: 92% said they would request a test if they developed symptoms, and 49% said they had taken a test in the previous seven days. Meanwhile, 57% said they would stay at home for 10 days if they developed symptoms.

Last year students were often accused of spreading the virus by holding parties in breach of restrictions, and some were fined and threatened with exclusion from their university studies.

Tim Gibbs, the head of the ONS student Covid-19 insights survey, said: “It is encouraging, the majority of students report being vaccinated against Covid-19, and many would get tested if they developed symptoms. However, a third of students sadly reported their mental health and wellbeing had worsened since the start of the autumn term.”

Nick Hillman, the director of the Higher Education Policy Institute thinktank, said: “This shows that students are largely very sensible – they are getting tested and vaccinated and they are trying to progress with their studies as best they can. But they are not finding life as easy as they had hoped because student life continues to be so disrupted by Covid. Going away to university is a big transition point at the best of times; it is extra stressful in the very odd times in which we live.”

Students at 58 institutions face the possibility of further disruption to their studies because of threatened strike action by university staff who voted in favour of industrial action in two ballots over pensions and pay and working conditions. The University and College Union will meet later this week to decide on its plans.