More than half of Scottish voters believe violence against MPs is a "price worth paying" to get their way on Brexit .
An investigation by researchers from University of Edinburgh and Cardiff University found both believed violence could be "worth it" if it meant their views prevailed.
The findings come among concerns among MPs on both sides of the debate that they are facing rising levels of abuse and threats from members of the public.
In 2016, prominent remain campaigner Jo Cox was murdered at the hands of a far-right extremist.
The survey's co-director Professor Richard Wyn Jones said he was "genuinely shocked" at the findings.
The survey, based on polling by YouGov, found 60 per cent of Leave voters in Scotland, 71 per cent in England and 70 per cent in Wales believed violence towards MPs was a "price worth paying" for Brexit.
Among Remain voters, 53 per cent in Scotland, 58 per cent in England and 56 per cent in Wales considered violence towards MPs was a "price worth paying" for Britain to stay in the EU .
Voters on both sides said protests in which members of the public are badly injured were a "price worth paying" to secure their desired outcome.
Among Leavers, it was 62 per cent in Scotland, 69 per cent in England and 70 per cent in Wales. On the Remain side, it was 56 per cent in Scotland, 57 per cent in England and 57 per cent in Wales.
Professor Wyn Jones said: "It's not often that one finds oneself shaken by research findings, but in this case it's hard to not be genuinely shocked – not only by the fact that so many think that violence is a likely consequence of Brexit, but that so many on either side of the Brexit divide seem to think that such events might be 'worth it' in order to secure their preferred outcome.
"Given that we appear to be on the brink of another general election in which further polarisation could be a deliberate campaign strategy for some parties, these findings should give all of us pause for thought and underline the importance of responsible and measured debate."
- YouGov surveyed 1,006 adults aged 18 in Scotland, 1,594 in England and 1,503 in Wales. Polling was conducted online between September 27 and October 3.
