Wilders is the leader of the Dutch Freedom Party (PVV).
Wilders has called the decision "cowardly", and said he still planned to enter the UK, vowing to board a flight to London on Thursday.
"This is something you expect in Saudi Arabia but not in Britain. I think this cowardly position of Britain is very bad," he said.
Lord Pearson, who invited Wilders to show Fitna at the House of Lords, said he was "very surprised" at the news.
Maxime Verhagen, the Netherlands' foreign minister, said his government would press Britain to reverse its decision.
Fitna is an Arabic word which has numerous meanings including "sedition" and "temptation", and appears in the Quran. In the film Wilders urges Muslims to tear out "hate-filled" passages from the text.
Its screening prompted protests in Pakistan, Iran, Indonesia and Afghanistan, while Ban Ki-moon, the United Nations secretary-general, described the film as "offensively anti-Islamic".
Wilders also sparked outrage over other anti-Islamic comments, including calling for a ban on the Quran and comparing Islam to Nazism.
Last month a court in Amsterdam ruled that he must stand trial for hate speech.