Mr Eriksen was reported to have written comments on a blog
The BNP has withdrawn one of its London Assembly candidates after he reportedly wrote that it was a "myth" that rape was a serious crime.
Nicholas Eriksen was reportedly behind a blog which suggested women were more troubled by handbag theft than by rape.
On Wednesday London Elects, which is overseeing the election, confirmed he had been withdrawn as a candidate.
Mr Eriksen was condemned in the Commons when Tory MP Charles Walker said he was not "fit to run for public office".
Deputy Labour leader Harriet Harman, standing in for Gordon Brown at prime minister's questions, replied: "I strongly support your comments and I thank you for bringing this matter to the House."
She added: "The best way to avoid a BNP member being elected to the London Assembly is to make sure that as many people as possible vote for all the other parties."
Mr Eriksen had been the second of the BNP's candidates for the London-wide list, which allocates 11 seats on the basis of proportional representation.
London Elects said that, following his withdrawal, other BNP candidates had moved up on the party's list.
Robert Bailey is now the BNP's second choice, after Richard Barnbrook, who is also running for mayor.
The Evening Standard reported that Mr Eriksen was the author of a far-right blog on which he had written: "Rape is simply sex. Women enjoy sex, so rape cannot be such a terrible ordeal.
"To suggest that rape, when conducted without violence, is a serious crime is like suggesting that force-feeding a woman chocolate cake is a heinous offence.
"A woman would be more inconvenienced by having her handbag snatched."
In a statement on the BNP website, the party said Mr Eriksen had "taken responsibility and unlike other politicians faced with similar circumstances has acted swiftly and honourably to resolve this matter".
Freedom and responsibility
It said: "It was felt that no matter how much Nick Eriksen's blog comments, written back in 2005, had been distorted and taken out of the context of a blog which reflected our tough stance on all sorts of crime, they could still be perceived as trivialising the issue in a manner that many women in particular could have found extremely offensive."
It added: "Whilst this party remains committed to free speech it should be understood that with that freedom comes responsibility."
There are 14 constituency seats on the London Assembly, elected through the first-past-the-post system. The London-wide list of 11 seats are divided according to the percentage of votes each party has won.
Any party that gets 5% of first choice votes is in with a chance of an assembly seat under the system.
At the last London elections the BNP got 4.8% of the vote and the party is confident it will get at least one seat this May.