It continues: "While an exception has been made in this instance, any future application you submit must be completed as accurately as possible, otherwise there is a risk that future applications may be refused."
Ai said yesterday: "This decision is a denial of my rights as an ordinary citizen." It means he will not be in the UK when China's President Xi Jinping makes a state visit in October, prompting speculation that the refusal was politically motivated.
The 57-year-old artist yesterday arrived in Germany after it granted him a four-year multiple entry visa to visit his 6-year-old son.
Maya Wang, a China researcher for campaign group Human Rights Watch, said the Government "appears not to have done its homework" and the decision was "politically motivated".
James Savage, a director at Amnesty UK, added: "While on this occasion this could be an administrative error that we hope will likely be swiftly rectified, Ai Weiwei's case does speak to a wider problem. The Chinese authorities routinely charge and convict human rights defenders with spurious, politically motivated criminal offences, for precisely the reasons this case illustrates, to tarnish an individual's reputation and make it difficult for them to travel freely and raise their concerns internationally."
When the Daily Telegraph asked the Home Office to explain why it claimed Ai had a criminal conviction, a spokesman said: "Reports that Mr Ai has been refused a visa are incorrect."
Later, the spokesman added: "This case did not come to the Home Secretary, and she is now looking into it."