China's best known contemporary artist abroad, Ai was detained for 81 days in 2011.
His company was fined USD 2.4 million the following year after losing a civil legal battle against tax authorities, proceedings widely seen as a reprisal for his outspoken criticism of the ruling Communist party.
Ai posted a letter on Instagram apparently from the visa section of the British Embassy in Beijing that stated it was "a matter of public record that you have previously received a criminal conviction in China, and you have not declared this," adding he had "exceptionally" been granted a visa for his stated travel dates.
Ai said in a separate Instagram post he had "never been charged or convicted of a crime".
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The artist added he had attempted to clarify the situation with British authorities "over several telephone conversations, but the representatives insisted on the accuracy of their sources and refused to admit any misjudgment".
Ai also posted a picture of his British visa, marked "Leave to enter outside the rules".
"This decision is a denial of Ai Weiwei's rights as an ordinary citizen," he added.
But it means he will not be in Britain when China's President Xi Jinping pays a high-profile state visit in October.
In a statement, Britain's Home Office said visa applications were considered "on their individual merits and in line with the relevant legislation", adding: "Mr Ai has been granted a visa for the full duration of his requested dates of travel."
Authorities confiscated Ai's passport after his 2011 detention, apparently attempting to limit his international influence, but police returned the document earlier this month.
Ai and his legal team said the tax case was rife with violations of legal procedure, and rights groups such as Britain's Amnesty International suggested it was politically driven and showed China's "deep insecurity."
Britain's governing Conservative party has sought to improve relations with China after leader David Cameron angered Beijing by meeting with the Dalai Lama.
Since then London has made a number of moves which have bought it back into Beijing's good graces, including joining the Chinese-led Asian Infrastructure Investment Bank, unlike the US or Japan.