Another member of the group, Jack Renshaw, was reported to the police last year by the CST for antisemitic comments he made in several of his speeches.
In one speech, Mr Renshaw said: "Hitler was right in many senses - but you know where he was wrong? As nationalists we need to learn from the mistakes of the National Socialists and we need to realise, you do not show the Jew mercy."
In a second, he said Britain took the "wrong side" in the Second World War by fighting the Nazis "who were there to remove Jewry from Europe once and for all".
The four men were arrested this morning in Birmingham, Powys, Ipswich and Northampton.
The police released a statement confirming that “the arrests were carried out with West Midlands Counter Terrorism Unit in conjunction with the Wales Extremism Counter Terrorism Unit and the East Midlands CTIU.
“A number of properties are being searched in connection with the arrests. The arrests were pre-planned and intelligence-led; there was no threat to the public’s safety.”