I genuinely don’t know the answer to that question.
Paul Mason’s blurb, on the BBC website, certainly doesn’t suggest that he was an activist in any extremist political party: although his Wikipedia entry says that he is ex-Workers Power.
What I do know is that last month, he took part in a meeting staged by the SWP front organisation “People Before Profit” alongside “SWP/Left Alternative supporter”, Graham Turner. His book was launched at the SWP bookshop. He spoke at the SWP conference in 2007.
Very many people were members of extreme and silly political parties in their youths*. Andrew Marr, for example, was in Socialist Organiser. To be frank, most revolutionary socialist groups are pretty inoffensive, and do no real harm.
That cannot be said about the Socialist Workers’ Party: which in the past ten years has devoted its energies to promoting speakers from Hamas and Hezbollah, lying about their genocidal racism, and promoting the viciously antisemitic Gilad Atzmon.
I do not think that a BBC journalist would participate in three events organised by the BNP or BNP front organisations. I am suprised that Newsnight’s Economic editor – of all things! – feels comfortable participating in SWP events.
* Not I!
UPDATE
My correspondents think that Paul Mason is still a Workers’ Power member. However, Wikipedia notes that in 2006, Workers’ Power expelled a third of its membership for “plotting”. So he might possibly have been chucked out of the party.