"Barmy Arthur" refers to Arthur Scargill, the leader, at that time, of the UK "National Union of [Coal] Mineworkers".
He tried twice to bring the UK to its knees with strikers, in the UK coal mines, demanding pay rises far in excess of inflation. Now there is virtually no coal mining industry left in the UK.
What the author is saying is here comes another set of union leaders, similarly looking for increases in pay in excess of inflation.
Hope this helps