The BBC has come under renewed pressure over its decision to invite the leader of the British National Party (BNP) to take part in BBC1's Question Time after the far-right party attacked non-white members of the panel.

Anti-fascist groups said last night that the corporation should rethink the inclusion of Nick Griffin in Thursday's broadcast after "racially-termed" insults were made against his fellow panellists Baroness Warsi, the shadow communities minister, and the black playwright Bonnie Greer.

Its attack on Lady Warsi, the last panellist to be announced for the programme, was posted on the party's website. "True to her Yorkshire roots [sic], she likes to call a spade a spade or a shovel even," the profile states, adding that, "the Baroness is 'bursting with ideas on how to bring together communities,' but curiously she doesn't tell us what those ideas are. My guess is she's planning coffee and (halal) cake mornings at the Markasi mosque in Savile Town" [in her home town of Dewsbury].

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The party had earlier published a similar profile of Ms Greer, accusing her of being a "black history fabricator" after she made a radio programme called In Search of the Black Madonna. "What does Bonnie Greer have to do to get on to Question Time?" the BNP website asked. "Answer: Fabricate black history and be paid for it ... The reality is that none of the 'black Madonnas' of medieval Europe even remotely resemble, in facial features, black people." It also described Jack Straw, the Justice Secretary who will be appearing for the Government, as "slimy".

The anti-fascist group Searchlight said that the BBC should reconsider its position. "The BNP uses racial language, describing Bonnie Greer as a black history fabricator and smearing Sayeeda Warsi," said a spokesman. "Regardless of the rights and wrongs of the decision to invite the BNP on to Question Time in the first place, it is another thing to start abusing fellow guests in racial terms. Surely the BBC cannot ignore this."

A spokesman for the BBC said: "It is not for us to comment on content on the BNP's website."

Mark Thompson, the BBC's director general, yesterday stood by the corporation's decision to invite Mr Griffin on to the programme. He rejected concerns raised by Peter Hain, the Welsh Secretary, that the BBC could be acting unlawfully by allowing the BNP to take part. A letter from Mr Hain had suggested that the BNP's current constitution, banning black, Asian and Jewish members, meant that it was in breach of the Race Relations Act.

"According to the advice we have received, the BNP is not prevented from continuing to operate on a day-to-day basis and its elected representatives continue to sit on councils and in the European Parliament," Mr Thompson wrote in reply to Mr Hain. "It remains the BBC's obligation to scrutinise and hold to account all elected representatives and to do so with due impartiality. We are also advised that if there were to be any election tomorrow, the BNP would still be able to field candidates."

Mr Straw is to appear on the programme despite the concerns of Mr Hain and the Home Secretary, Alan Johnson, who refused to take part. Downing Street said the decision to invite the BNP was one for the BBC. A No 10 spokesman added that Mr Straw's decision to take part was "not a problem".

Concerns over the inclusion of Mr Griffin are growing within the Labour Party, however. Jon Cruddas, a Labour backbencher who has never shared a platform with the BNP, said that the corporation should not have used Question Time to give the party publicity.

"While they have to give them a platform, the question is what platform," Mr Cruddas said. "Question Time is precisely the wrong format for them to use, because it lends itself to sound-bite populism. There are four other panellists and the format avoids scrutiny and in-depth dissection of people's positions. They could still have acknowledged the fact that BNP voters pay for their licence fee by giving Nick Griffin 45 minutes with John Humphrys or Andrew Neil."

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Should Griffin be allowed on? The debate rages ...

Refusing the BNP a platform has stopped working: Ed Husain, Co-founder of the counter-extremism think tank Quilliam Foundation

A no-platform policy for the BNP has failed. Fifty councillors across Britain, two MPs in Brussels and one GLA member show that the "no-platform" consensus of Britain's political class is outdated. That's not to say it was wrong – it was right for its time and helped to make the BNP moderate its views.

But what now? Griffin has cut his teeth in northern cities and specialised in launching semantic attacks on Muslim communities to which very few Westminster politicians can respond with similar audacity, oomph, and conviction. How many know the difference between a Sunni and a Shia Muslim? What will Jack Straw say when Griffin launches a tirade against communal separatism in Straw's constituency, Blackburn?

Do our politicians have the courage to talk about immigration, class, Europe with the candour of Griffin? I doubt it.

Combined with the broadcast media's hunger for sensationalism, Nick Griffin has this Thursday's debate game, set and match. If all goes well, Griffin's real opposition is not Straw or Chris Huhne, but Baroness Sayeeda Warsi who can, and should, ask in all candour: "What's un-British about me, Griffin?" All power to Sayeeda. Tories, watch and learn.

The BNP are racist and laughable – but still get away with it: Douglas Murray, Author and the director of the Centre for Social Cohesion

Nick Griffin represents a fascist party which can now claim to speak for almost a million voters. This shows, among other things, that the Unite Against Fascism style of left-wing anti-BNP tactics has failed. On Thursday night UAF will hold a demo outside the BBC while the fascist Griffin sits inside on the panel.

We have to rethink the way in which we critique the BNP. Their ideas divide into the laughable and the racist. Thursday should provide an opportunity to show this, but I suspect it won't.

Politicians on the panel will spend their time running to the opposite end of the see-saw to Griffin. The only way to take the BNP apart is to explain that there are legitimate reasons for people in the UK to be worried about immigration and the future of our country but that Griffin is a racist and exactly the wrong person to deal with that.

Our government and opposition – epitomised by fellow panellists, Jack Straw and Sayeeda Warsi – have spent years cosying up to Islamic fascists. Now they have the chance to meet the nativist variety this has given succour to. I only wish they knew how to destroy what they have helped create.

The BNP succeed because MPs ignore awkward issues: Roger Scruton, Philosopher and broadcaster

Questions of the greatest concern to ordinary voters in our country are either swept aside by politicians of the mainstream parties or ruled out as undiscussable. Immigration, and the cost of it; the European Union and its effect on our way of life; the nation and its identity; and so on.

When the mainstream parties refuse to discuss issues of common concern, and when prominent people are intimidated into dissociating themselves from anyone who nevertheless does so, new political parties will emerge, which make those issues central to their identity.

The élites then close ranks, to prevent those new parties from obtaining a public voice or a shared platform. Are the people well served by this?

Should we not be making sure that the BNP has a voice in politics, so that the main political parties are compelled, at last, to come into the open concerning matters which are of the greatest concern to the people? Of course, it may be that the BNP is advocating illegal, subversive or unconstitutional measures: in which case it should be silenced by law, and not by censorship.

Nobody, so far as I know, has suggested that this is so. The "no platform" approach is therefore essentially anti-democratic, and deeply insulting to the many British subjects who would like the questions raised by the BNP to be publicly discussed by the only people – the politicians – who are in a position to address them.

Griffin is slippery and will be very difficult to pin down: Ann Cryer, Labour MP for Keighley

I found out that Nick Griffin was standing against me in the 2005 general election a few weeks after the death of my husband in a car crash. He was the last person I wanted to hear from at that time in my life.

I have spent 12 years walking on egg shells because of my work to fight the cases of Asian young women, and not wanting that work to be twisted by the BNP so they could use it against the Asian community in my constituency. I have always refused to share a platform with the BNP and I continued to refuse during that election.

My mind is divided over his appearance. Nick Griffin is a slippery politician. He will say one thing to supporters on the doorstep and something else to the media. I find him completely distasteful. But I have no problem with someone going on the programme if they think they can benefit the cause of democracy by demonstrating to the public just what it is he is about.