When Carrie Paechter, a professor at Nottingham Trent University, tweeted two weeks ago that students could register to vote at both their home and term-time addresses, she didn’t anticipate the tirade of anger it would unleash. She was reported to the police and the Electoral Commission, and someone wrote to her vice-chancellor calling for her to be disciplined.

Prof Paechter, who is director of Nottingham Centre for Children, Young People and Families, posted what she thought was an innocuous tweet on a Thursday evening. By Sunday she had blocked 568 people on Twitter who were furiously accusing her of encouraging students to break the law and vote twice. She insists she had no such intention, and simply wanted to ensure students didn’t miss out on voting in the general election, because they didn’t know their rights.

“I didn’t mention tactical voting and I didn’t think I’d said anything remotely controversial. I was just reminding students of their democratic right. I was really surprised by the storm I found myself in the middle of,” she says.

One angry reply to her tweet said: “Enticing people to commit fraud is a criminal offence that can include a prison sentence. Not very good for your career prospects.” Another said: “You’re encouraging illegality and bullshitting about your motives. Do you think we’re all stupid?”

The student vote will be crucial in some constituencies. This term, for the first time, universities have welcomed three whole years’ worth of students – first, second and third years – who were too young to vote in the European referendum in 2016. Three-quarters of students feel the country was wrong to vote to leave the EU, and half of those whose vote is likely to be affected by Brexit said they would be prepared to vote tactically, according to a Youthsite poll published by the Higher Education Policy Institute thinktank last week.

Professor Carrie Paechter of Nottingham Trent University had to block 568 people on Twitter after her attempt to get students to register to vote Photograph: Andy Sutton

Academics across the country are taking their own measures to ensure students make their voices heard. Some are using lectures to encourage them to register to vote, others are hitting campus with iPads and signing students up themselves.

Prof Paechter says she has always been careful to keep her personal views on Brexit out of social media, but she is unrepentant about trying to spread the word about voting rights. “Universities have a responsibility to raise these issues with students. There is much less awareness of where you can vote than there used to be.”

She is not the only academic to face vitriol on social media for talking about student voting. One lecturer was told by his university that he could only talk anonymously to Education Guardian about encouraging students to vote because of the heat this was drawing online. “The anger I’m still getting on Twitter is quite astonishing,” the lecturer says. “Clearly some people are against any kind of student vote. I’ve been accused of patronising my students by telling them how to vote, which is ridiculous because for most of them it’s the first time they’ve done it.”

The lecturer says informing students they can register in two places– although they can only vote in one – is pointing out the law, “not some sneaky loophole”.

“We don’t officially break up until 13 December, but at the end of term it is never clear cut what students will be doing,” he explains. “Some will have jobs at home or just want to see family – Christmas is a key time for homesickness – so they may leave early.”

Smita Jamdar, head of education at the law firm Shakespeare Martineau, points out that unlike in the past two general elections, universities now have an explicit legal obligation to encourage students to sign up to vote, as a condition of being accredited by the Office for Students. Jamdar says: “Even if they haven’t been directed to do this by their university, academics have freedom of speech and there is nothing unlawful about encouraging other people to vote.”

Johanna Anderson, a librarian at the University of Gloucestershire, was putting posters up in the library about registering to vote even before the election was called. Now she has recruited a group of about 30 academics, support staff and students to take an iPad around the university’s three campuses in between lectures to sign students up. “The impact of this election is going to be monumental and I think it would be completely irresponsible of us not to encourage our students to take part,” she says.

Cheltenham is seen as one of the marginal seats that could define the election. It is currently Conservative, but backed remain in the referendum and is a key Liberal Democrat target.

Anderson says: “A lot of students have said they are already registered at home and they had no idea they could register to vote here too. We are letting them know that we are in a really marginal seat here so their vote can really make a difference.”

The electoral office in Cheltenham has phoned to thank her, following a spike in registrations since her team hit the campuses.

Oxford West and Abingdon is another electoral battleground where the student vote may be critical. The Lib Dems won it back from the Tories in the last election with a slim majority of 817.

At Oxford Brookes University, Hermione Ruck Keene, senior lecturer in creative curriculum and primary education, is planning to use her classes to check whether students are registered to vote. She will also ask first-year students in one module to research their local MP’s position on arts education.

“It is so important that everyone votes,” she says. “The timing of the election potentially means that students could miss out on voting. I want to help ensure they don’t.”

Meanwhile in Fife North East, the Scottish National party is defending a majority of only two votes over the Liberal Democrats. At St Andrews University Stephanie O’Rourke, a lecturer in art history, teaches 300 first- and second-year students and has been including slides on how to vote in her lectures. Her department has emailed 500 students calling on them to vote.

She believes this election could have an “historic” impact on students, citing the future of tuition fees, whether the NHS will have the capacity to deal with student mental health problems, and, post Brexit, “whether their lecturers will stay in the UK”.

But some are concerned that academics may try to influence how students vote. Helena Cowell, a parent from Macclesfield, says: “My daughter was in a seminar with about 20 students at Keele University last week. They discussed whether they had all registered to vote, then the seminar leader said ‘So you are going to vote for remain parties aren’t you?’”

Cowell is annoyed. “Encouraging them to vote is a good thing but saying something that might cause peer pressure and not open it up for discussion is wrong.”

A spokesperson for Keele said: “We encourage students to vote but do not direct them to support any particular party.”