///The question that must be asked is why being a member of this particular group is against the law?///
I found this, very poorly concealed, at the end of the Link you gave in the OP.
///National Action became the first extreme right-wing group to be banned under terrorism laws in December 2016.
The proscription meant that being a member of or inviting support for the organisation is a criminal offence carrying a sentence of up to ten years in jail.
In the official list of proscribed groups, it is described as a 'racist neo-Nazi group' that was established in 2013 and has branches across the UK which 'conduct provocative street demonstrations and stunts aimed at intimidating local communities'.
The document adds that the group is 'virulently racist, anti-Semitic and homophobic' and says its activities and propaganda materials are particularly aimed at recruiting young people///