Home Secretary Theresa May "was not consulted over the decision to grant Mr Ai a one-month visa", a spokeswoman for her department said.
"She has reviewed the case and has now instructed Home Office officials to issue a full six-month visa. We have written to Mr Ai apologising for the inconvenience caused."
Campaigners noted that the previous visa would have allowed Ai to attend an exhibition of his work at London's Royal Academy from September but meant he would not be in Britain for Chinese President Xi Jinping's state visit in October.
After he finally received his passport last week, Germany granted him a four-year multiple entry visa but Ai said on Thursday that Britain had denied his request for a six-month visa and restricted him to a three-week trip because he did not declare a "criminal conviction".
Ai said he had "never been charged or convicted of a crime".
Jigme Ugen, head of a US-based Tibetan rights group, described the initial decision to grant Ai a shorter visa as "purely a kowtow to Xi Jinping's London visit".
