Here's a recent report on left-wing extremism in the United Kingdom:
https://assets.publishing.service.gov.uk/government/uploads/...
I have not found a similar study on far-right extremism but there is a report giving an overview of the far right:
https://assets.publishing.service.gov.uk/government/uploads/...
Reading these reports shows that political violence currently is at a low level in the UK but that it is on the rise internationally which has the potential to lead to an increase both on the far-left as well as the far-right side.
Section 3 of the link breaks down how many people have been identified as at risk from particular ideologies.
'Mixed, unstable or unclear' accounts for 51%.
Islamic extremism is 24%.
Right-wing extremism is 22%.
Left wing extremism is less than 3%.
So, the data aligns well with what the original commentator was suggesting.
[0] https://www.gov.uk/government/statistics/individuals-referre...
Are we talking about the same United Kingdom as the one where Yougov has been doing polls on the subject of extremism [1]? If so I wonder what gives you the impression that the bulk of [y]our issues are growing far-right, nationalist, and/or authoritarian groups given that those who answered those polls come up with the following ranking:
#1 islamic extremism (58%)
#2 right-wing extremism (31%)
#2 left-wing extremism (23%)
Unsurprisingly the results differ widely based upon the political affiliation of the interviewee with left-wing voters placing larger emphasis on right-wing extremism while right-wing voters do the opposite. Nevertheless, left-wing extremism seems to be almost as 'popular' as the right-wing version while both are far less 'popular' than islamic extremism.
[1] https://yougov.co.uk/topics/politics/articles-reports/2021/0...