After his performance was widely panned in the press, he denounced the "unfairness" of the way the programme was produced and called on the BBC to give him a second chance to appear, talking about the issue of the day.
"The British public are aghast at the display of bias from the BBC, the venom form the political class, and the sheer unfairness," he told a news conference.
"That was not a genuine Question Time, that was a lynch mob."
Mr Griffin said that the BBC had deliberately changed the format of the programme to concentrate on him and his policies.
He said that the party was now making a formal complaint to the BBC over the way in which the programme had been "twisted".
"People wanted to see me and hear me talking about things such as the postal strike. One or two questions about what a wicked man I am, fair enough, but the whole programme - it was absurd. Lets do it again but do it properly this time," he said.
He also said that he wanted to challenge Justice Secretary Jack Straw to a one-on-one debate on the issues of the day, and called on Tory leader David Cameron to disassociate himself from the protests outside BBC Television Centre where the programme was recorded.
Mr Griffin insisted that the programme should have been filmed somewhere else because London was "not my country any more".
"I think I did fine under the circumstances," he told reporters. "But overall my performance is not judged by me, it is not judged by the chattering classes.
"It will be judged and is already being judged by millions of ordinary Britons who saw one man speaking up and trying to explain how they feel, how the English feel when they are not even allowed their name on a census form, and that one man being howled down and dragged down by a pack."
He went on: "That audience was taken from a city that is no longer British...
"That was not my country any more. Why not come down and do it in Thurrock, do it in Stoke, do it in Burnley?
"Do it somewhere where there are still significant numbers of English and British people living, and they haven't been ethnically cleansed from their own country."
Mr Griffin added: "Demographically there is lots of support for the Lib Dems there because for instance they are regarded as the party of ethnic minorities.
"There is not much support for me there, because the place is dominated by ethnic minorities.
"There is an ethnic minority that supports me, the English. But there's not many of them left."
The BBC said it received more than 350 complaints after the show was broadcast last night by midday today - the bulk of which accused the show of being biased against the BNP and/or Mr Griffin.
More than 240 people felt the show was biased against the BNP, while more than 100 of the complaints were about Mr Griffin being allowed to appear on Question Time.
In addition, more than 50 people contacted the BBC to show their appreciation for the programme.
French far-right leader Jean-Marie Le Pen, who saw his support double overnight after appearing on a high-profile TV political discussion show in 1984, suggested the BNP could receive a boost from last night's programme.
Mr Le Pen, leader of France's Front National, told London's Evening Standard: "Small fish will become big so long as God gives them life.
"All political groups have started as marginal before becoming important."
Responding to the BNP leader's comments about the capital, London mayor Boris Johnson said: "Nick Griffin is right to say London is not his city.
"London is a welcoming, tolerant, cosmopolitan capital which thrives on its diversity.
"The secret of its long-term success is its ability to attract the best from wherever they are and allow them to be themselves - unleashing their imagination, creativity and enterprise.
"The BNP has no place here and I again urge Londoners to reject their narrow, extremist and offensive views at every possibility."
Mr Straw said that while it had been right to debate the BNP on Question Time, the political agenda should now move on.
"Mr Griffin was last night exposed as a fantasising conspiracy theorist with some very unpleasant views and no moral compass. But now that he has been exposed for what he is it is time to move on," he said.
"There is no denying that many people are disillusioned with mainstream politics. The imperative now is to engage with them directly and put the extremist BNP sideshow behind us."
The BNP claimed Mr Griffin's appearance on Question Time sparked the "single biggest recruitment night" in the party's history.
It said 3,000 people registered to sign up as members once a current recruitment freeze - introduced in response to legal action over the party's discriminatory membership rules - has been lifted.
A message on the BNP's website said: "This figure represents the single largest block of new membership expressions of interest ever, and will, once formally signed up, have boosted party membership by nearly 30 per cent."
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