How did sensation novels come to be accepted by the middle-class in the Victorian era?
Sensation novels started out as reading for the working-class who couldn't afford any better, so how did the come to be widely accepted.
This question is making an incorrect assumption. Sensation novels did not start as working class literature. The person submitting the question is confusing the sensation novel with the penny dreadful.
The sensation novels of the 19th century evolved directly from the 18th century gothic genre. They were sold mainly in triple decker format to circulating libraries (a middle class phenomenon). The first author to directly market her novels to the public in single volume format, was Marie Corelli, 1890s. The early sensation novels by Braddon, Ouida, Collins, Wood, etc. were all issued in triple decker format, far outside the economic reach of the lower classes.