Mr Griffin made the remarks after Ukip council candidate William Henwood told Lenny Henry to emigrate to a black country.
Griffin told the BBC: "If you look at Ukip they are using all our rhetoric, they are using our slogans, they are recycling our posters and people like it.
"The only difference is that Ukip won't deliver. Their actual policy is a 50,000 net increase in immigration every year.
"When they talk about balanced migration what Farage actually means is for every Brit who leaves Britain, they'd be happy to let a Pakistani or an Afghan in, which means their policy is actually about 300,000 new immigrants a year.
"Our policy is simple: shut the door, we don't want anyone - black, brown, green or white.
"I think if the public get to understand that then Ukip's vote is going to meltdown as they come under the scrutiny they deserve."