It was announced on Thursday that the couple, from Brampton in Cambridgeshire, had won their discrimination case against a B&B owner who refused to give them a room because they are gay.
In four messages posted online this afternoon, Mr Griffin described the couple as “bullying ‘gay’ activists” and appealed for someone to give him the couple’s address.
Mr Griffin, who is chairman of the BNP, then published the couple’s details and told them: “We’ll hold demo for rights of all home owners, gays included, to rent or not rent rooms to whomsoever they wish.”
He added: “A British Justice team will come up to Huntingdon and give you a bit of drama by way of reminding you that an English couple’s home is their castle. Say no to heterophobia!”
A spokesman from Cambridgeshire police said they had been made aware of the issue.
Mr Griffin was trending on Twitter following the posts, with a large number of people condemning his actions.