1816 "Alastor" was rejected by a library on grounds of immorality.
1822 In 1813, at 21 Shelley had published "Queen Mab, a philosophical Poem" in a very small private edition. In 1817 it was cited in his custody trial to show the author was an atheist and free-love advocate. In 1821 William Clarke issued an edition of "Queen Mab, a philosophical Poem" , and in 1822 he was prosecuted by the Society for the Suppression of Vice.
1840-1842 Edward Moxon, a leading publisher, began issuing Shelley's works. He and three other publisher-booksellers were prosecuted, partly to test if there was one law for "the low booksellers of the Strand" and another for more aristocratic ones, who were freely publishing books at least as outspoken as 'Queen Mab, a philosophical Poem'."
1840-1842: Moxon was released, but had to give up all copies of his edition.
One reason for official hostility to this book in this entire period was that it became a basic text for lower and middle-class radicals and for the Chartist and Owenite reform movements. The period of Shelley's life was an especially repressive one, politically, in Britain, a nation badly frightened by the French Revolution.
Source: Banned Books 387 B.C. to 1978 A.D., by Anne Lyon Haight, and Chandler B. Grannis, R.R. Bowker Co, 1978.