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The Church of England permitted nonconforming or dissident sects. They were not members of the CoE, but only the Roman Catholics were officially prohibited.
@T.E.D. questions whether it was illegal to be Roman Catholic. The situation is not entirely black and white, but
After a brief experiment with Protestantism under his son Edward VI (1547-53) and a brief return to Catholicism under his elder daughter Mary I (1555-58), England officially became Protestant in 1559 under his younger daughter Elizabeth I (1558-1603). Except under the Catholic James II (1685-88), Catholicism remained illegal for the next 232 years. Papal Visit
Not precisely an unbiased source, so....
Another Act of Supremacy was passed in 1559 under Elizabeth I, along with an Act of Uniformity which made worship in Church of England compulsory. Wikipedia
@T.E.D provides the following links
(I've marked this community wiki to permit others to contribute to the full picture of religious predjudice at the time. I believe that although the OP asked a focused question, a real answer requires a broader understanding).
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"The Man Who Laughs" is set in England during the 17th century (not 18th). It was a time of religious conflict, with for example James II being Roman Catholic and taking steps towards religious freedom. The church did not have a strong grip on peoples religions at this time.
Heresy was indeed illegal, but it is not automatically heretical to have your own religious group and meetings. Heresy was more strict than that. So there was definitely several religious groups in England at this time. Some of them were persecuted, and this in fact was a strong incentive for some people to move to the American colonies. But not all groups were persecuted, because not all non-conformism was heretical.