Michael Black and John Morgan, the gay couple on the receiving end of abuse from Nick Griffin, say they will not press for charges against the BNP leader.
Last Thursday, Mr Griffin published the Cambridgeshire address of Mr Black and Mr Morgan on Twitter and called for a demonstration to be held outside their home.
Mr Griffin, who is also an MEP for the North West, has refused to apologise for his behaviour and has now launched an outspoken attack on the human rights campaigner Peter Tatchell and the organisation Liberty.
According to Cambridge News, at the start of the weekend a police guard was placed outside the Brampton home of Mr Black and Mr Morgan.
Mr Black told the paper: “We think it is just hot air – empty bombast.
“When we first heard about the tweet we felt rather apprehensive about it, John more so than I.
“We rang the police and they were extremely helpful. They sent someone round to keep an eye on the house and to have a word with neighbours.”
Mr Black added: “We decided that we did not want to make an official complaint.
“I have been openly gay for 37 years living at this house. I have never had any trouble of any kind.”
Richard Howitt, Labour MEP for the East of England, said:
“All this couple were doing was standing up for their rights. This must be very frightening for them.”
A spokeswoman for Cambridgeshire police said there had been no reports of any demonstrations and that investigations were continuing.