Some 25 anti-fascist activists broke through police lines and made it into the building ahead of the far-right politician's arrival.
Traffic outside Television Centre in White City, west London, ground to a halt as hundreds of campaigners demonstrated against Mr Griffin's presence on the Question Time panel.
Speaking after entering the building, Mr Griffin said of the protesters: "I was rather expecting that.
"The Labour Party financed groups from all over the country bringing a mob down here today. It was always going to be a fairly big event."
The BBC confirmed some of the demonstrators were able to breach security but said the disruption was dealt with promptly.
A spokesman said: "A small number of people managed to get into Television Centre.
"However, they were identified and are being escorted from the building quickly."
The scuffles began just before 4.30pm as the protesters were on an impromptu march down Wood Lane in front of Television Centre.
Security guards opened a gate to let a car into the front car park and about 30 people jumped over the barrier and ran towards the building.
Lukas Keudic, 20, a student at King's College London, managed to get to the doors of the studio where the controversial debate was being filmed.
He said: "We were in the main reception next to Piers Morgan when about 30 police officers turned up.
"There were about 10 to 20 of us and we were just standing there chanting in a peaceful protest.
"We spoke to the police and they started grabbing us. They grabbed one person and we started chanting 'Ian Tomlinson' and then they put us into a corner."
Members of the Question Time audience were escorted into the building after having their passports checked.
Among them was Frank Langan, 66, from Ealing, west London, who said: "I'm going to go in and find out what Nick Griffin has got to say.
"I don't have to agree with it but I think it's right that he is allowed on Question Time. I think everybody is entitled to their own opinion, even if you don't like them."
As the protests grew, Mr Griffin predicted that tonight's Question Time would be "political blood sport" but said it could propel his party into "the big time".
In an open letter to BNP supporters, he said his appearance on the flagship BBC1 political show was an unprecedented chance to present their views to the UK public.
BBC director general Mark Thompson challenged the Government to ban the BNP from the airwaves if it felt Mr Griffin should not be allowed to take part.
But Prime Minister Gordon Brown said it was a matter for the corporation and he did not want to interfere with it.
Mr Griffin said in his letter, posted on the BNP's website: "Question Time is scheduled for 10.35pm tonight and will be a milestone in the indomitable march of the British National Party towards saving our country.
"Our violent opponents on the far left have promised to lay siege and barricade the studio venue, because they know only too well that this could be THE key moment that propels the BNP into the big time.
"Never before have we had the chance to present our patriotic, common sense solutions to Britain's nightmare situation to the public at large in such a prominent fashion."
The far-right politician claimed Question Time would be "stage-managed" so the audience and panellists were "overtly hostile" towards him.
An appeal by Cabinet minister Peter Hain against Mr Griffin's appearance on the programme was thrown out yesterday by a special BBC Trust panel.
Mr Thompson today issued a strong defence of the decision to have the BNP on Question Time.
The BBC director general said the party's recent electoral success, which saw Mr Griffin elected as one of two BNP MEPs, meant it was right to invite him.
And he said only a legal ban, similar to that imposed on Sinn Fein in the 1980s, would lead the Corporation to consider breaching its "central principle of impartiality".
Mr Thompson wrote in the Guardian: "If there is a case for censorship, it should be debated and decided in Parliament. Political censorship cannot be outsourced to the BBC or anyone else."
Mr Brown said the appearance of Mr Griffin on the programme would present a good chance to expose his "unacceptable" views.
He told Real Radio in Yorkshire: "If on Question Time, they are asked about their racist and bigoted views that are damaging to good community relations, it will be a good opportunity to expose what they are about."
Asked whether Mr Griffin should have been invited on to the programme, Mr Brown said: "It was a decision of the BBC. We are not trying to interfere with the decision of the BBC."
The Prime Minister defended the decision to break with Labour's previous practice of refusing to share a platform with the BNP and to allow Justice Secretary Jack Straw to debate with Mr Griffin tonight.
"The issue is: should we have someone there? Jack Straw is a very experienced person who has had to deal with the BNP and their awful politics over a period of time," he said.
"I hope that the exposure of the BNP will make people see what they are really like."
The demonstration outside Television Centre was organised by Unite Against Fascism.
Weyman Bennett, the group's joint national secretary, said: "I don't believe the BNP are going to be taken apart in the debate.
"What they are going to get is a massive hustings for their fascist and racist politics and the price for that will be an increase in the number of racist attacks."
Labour MP Andy Slaughter, whose constituency includes Television Centre, was outside the BBC this morning to lend his support to the protesters.
He said: "I think it is just irresponsible.
"Cutting through the dinner party conversation about freedom of speech, the practical impact it is going to have on Muslim, black and Asian communities is reason enough not to give the BNP a platform."
Former London Mayor Ken Livingstone, chairman of Unite Against Fascism, insisted the BBC should not give Mr Griffin air time unless the courts ordered it to do so.
Also appearing on Question Time tonight are Mr Straw, shadow community cohesion minister Baroness Warsi, Lib Dem home affairs spokesman Chris Huhne and writer Bonnie Greer.
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