Police in Cambridgeshire have said they are investigating complaints made after the leader of the far-right British National party, Nick Griffin, posted the address of a gay couple on the internet and appeared to urge his supporters to demonstrate outside their home.

Michael Black, 64, and John Morgan, 59, a couple from Brampton, Cambridgeshire, had found out earlier on Thursday that they had won their highly-publicised civil case against a Christian bed and breakfast owner who had told them they could not stay in one of her double rooms due to her religious convictions.

Black, a writer and exams consultant, had told the Guardian he and his partner were delighted by the ruling from Reading crown court, which found that Susanne Wilkinson, owner of the Swiss Bed and Breakfast in Cookham, Berkshire, had been directly discriminatory in her treatment of the couple. She was ordered to pay £3,600 in damages, which Black and Morgan – who have been living together for six years and in a relationship for nine – said they would donate to charity.

But within hours of celebrations at what was seen as a significant vindication of equality legislation, gay rights activists were outraged by several messages on Twitter by Griffin, chairman of the BNP and an MEP, in which he made public Black and Morgan's address and claimed a "British Justice team" would come and protest the ruling at their home.

The first messages read: "If anyone can give us address of the 2 bullying 'gay' activists who've won case v Christian B&B owners, we'll hold demo … for rights of all home owners, gays included, to rent or not rent rooms to whomsoever they wish."

Two hours later, Griffin posted the following tweet: "A British Justice team will come up to [their Huntington address] & give you [Black and Morgan] a … bit of drama by way of reminding you that an English couple's home is their castle. Say No to heterophobia!"

The comments sparked anger. LGBT Labour, the party's campaign for gay rights, urged people to report Griffin for allegedly breaching the Communications Act 2003, under which it is an offence to post menacing messages on the internet. Others said they had reported his comments to the Metropolitan police's internet hate crime unit.

A spokeswoman for Cambridgeshire police said it was looking into "a number of complaints" it had received about the tweets. Officers had been in contact with the men and would visit them on Thursday night, she said. A spokesman for Stonewall, the gay rights campaign group, said: "This is beyond words unbelievably shocking. It is a real example of the hatred still out there towards gay people. We assume the couple concerned will make immediate contact with the police to guarantee their safety."

Griffin then wrote: "Why don't left & gay activists confront Muslims instead of picking on meek & forgiving Christians? Bullies are always cowards!"

Twitter users trying to access Griffin's account were subsequently told it had been suspended.

Black and Morgan, a computer consultant, had spoken of how their treatment at the Cookham B&B in March 2010 had made them feel "like second-class citizens". But Black said he hoped their victory would serve as proof that discrimination against any minority was no longer permissible. "We're doing this to try and make sure that all B&B owners realise what the law is and think twice before discriminating against gay people, black people, Christians, Muslims, Irish, any other group."

Asked how he had reacted to being refused access to the B&B, Black said: "It felt as if we were being treated like second-class citizens. I was shocked that it had happened. If it had happened 30 or 40 years ago it would have been far less surprising because discrimination was much more overt and common then. But for it to happen nowadays was a shock. I think the great public support we received as a result of it shows that we were right to be shocked – that it's only a minority, a small minority, who feel that gay men and women are sinners and that they can't allow us to sleep under their roof."

In the ruling, Recorder Claire Moulder said that, although the court recognised the sincerity of Wilkinson's religious beliefs, the owner had treated Black and Morgan "less favourably than she would treat unmarried heterosexual couples in the same circumstances" and had therefore broken equality law.

Wilkinson – whose legal defence was paid for by the Christian Institute, a national charity – said she was giving "serious consideration" to an appeal against the ruling.

"Naturally, my husband and I are disappointed to have lost the case and to have been ordered to pay £3,600 in damages for injury to feelings. We have the option to appeal, and we will give that serious consideration. We believe a person should be free to act upon their sincere beliefs about marriage under their own roof without living in fear of the law. Equality laws have gone too far when they start to intrude into a family home."

Lawyers for Wilkinson argued that she was entitled to refuse double rooms not only to gay couples but also to couples who were not married or in a civil partnership. Black and Morgan are not in a civil partnership.

Wilkinson and her husband say they have received two years of abuse for the decision, which enraged gay rights campaigners but gave succour to some Christians' claims of persecution.

In her statement, Wilkinson said: "People's beliefs about marriage are coming under increasing attack, and I am concerned about people's freedom to speak and act upon these beliefs. I am a Christian, not just on a Sunday in church, but in every area of my life – as Jesus expects from his followers.

"That's all I was trying to do and I think it's quite wrong to punish me for that, especially after enduring over two years of vile abuse and threats. We find this a strange justice in a society that aspires to be increasingly tolerant."