Published on Friday, 19 October 2012 11:54 Written by SKy News
The MEP published the address of Michael Black and John Morgan on the social networking site and called for a demonstration to be held outside their home.
Cambridgeshire Police said on Thursday it was investigating the incident and Dyfed-Powys Police said it was liaising with the force.
The tweets, under the username @nickgriffinmep, followed Mr Black, 64, and his 59-year-old partner Mr Morgan's win against the owner of bed and breakfast accommodation who refused to let them stay in a double room because of her religious views.
The couple, from Brampton in Cambridgeshire, sought damages from Susanne Wilkinson after she turned them away from the Swiss Bed and Breakfast in Cookham, Berkshire, in March, 2010, even though they had made a reservation and paid a deposit.
One of the tweets read: "So Messrs Black & Morgan, at (their address). A British Justice team will come up to Huntington & give you a...
"...bit of drama by way of reminding you that an English couple's home is their castle. Say No to heterophobia!"
Mr Griffin told Sky News: "I was very angry in the way in which left-wing political activists and a minority of gay activists are working with left-wing judges to use the Human Rights Act to persecute ordinary people, especially Christians.
"I most definitely didn't post a menacing message and there's nothing inciteful, I said that we'd be holding a demonstration on behalf of everybody including gay people to decide who they have and don't have in their homes.
"I don't think that could be described as menacing.
"I only regret that we haven't so far found the address of the judge who made that outrageous judgement because when we do we'll be looking at a demonstration somewhere near that."
Mr Morgan said the tweets had made him feel "uncomfortable".
"We live in a reasonably small village and I don't think either of us expect a mass demonstration but we might be wrong."
Mr Black said Mr Griffin had misunderstood the law on discrimination.
"Nick Griffin has missed the point that the difference between what he's saying and the law is that if somebody opens a B&B that is offering a service to the public, it's a business, it's not a private home.
"Whereas everyone has the choice as to who to admit to their own home, if you're offering a service to the public you have to abide by the laws."
A Cambridgeshire Police spokeswoman said: "We have received a number of calls in relations to the tweets and are looking into the complaints we have received.
"Officers will also visit the men mentioned in the tweets as part of our inquiries."
The case at Reading County Court concluded the couple had suffered unlawful discrimination.
At the time, Mr Black, an exams consultant and writer, protested at their treatment but the owner refused to allow them to stay as it was "against her convictions".
Credit: Sky News