Yes, there are a number of banned neo-Nazi organizations in the UK. Combat 18 is probably the most well-known (British Movement, White Wolves...there are a few).
These groups are offshoots of political parties, as fascist parties started to splinter in the 90s as it became less acceptable to be overly racist/fascist. Under Tyndall the BNP, which was a political party, was very violent (Combat 18 supposedly provided "protection" for their rallies). No terrorism but organising attacks on minority groups certainly (in the early 90s before Nazi groups went underground, there was a strong link with football hooliganism as certain clubs had groups that were overtly racist...Birmingham's firm is the only one I am aware of that wasn't racist). Tbh, these groups are more like criminal gangs in the US than anything else (and they had very little electoral success until Griffin moved the party away from overt fascism).
Also, it is worth pointing out that Copeland was a member of the BNP. He was obviously a nutjob but he was closely associated with the party, and the overt racism/violent rallies was still part of the BNP until the late 90s (and even after Griffin took over).
The UK also had a brief period in the early 2000s, before Islamic terrorism really took off and after right-wing groups started to really lose steam, where environmental terrorism was the main source of attacks. Environmental groups sent anthrax to academics who experimented with animals, and groups (iirc, ALF) were trying to bomb animal testing facilities (that is why animal testing facilities in the UK usually have multiple rings of barbed wire 20ft high, guard posts, cameras everywhere...I actually live near one of these places, and it was built when this was picking up: no signposts at all, tiny one-car road down to the facility, forest completely surrounds it so you can't see it from anywhere else, not built near any main road).
Btw, the whole premise of the original argument is ludicrous...these groups know they are being watched. I am sure that online communications are used after suspect has been identified but indoctrination is largely happening within in-person groups. With Islamic fundamentalism, it is same mosques, it is the same groups of people. I don't think any level of surveillance will stop lone wolf attacks either.