Unlicensed betting shops (known as List Houses) flourished from the late 18th century until 1853.
In that year the Betting Houses Act was passed. This closed down the List Houses and drove betting into pubs until they too came under the same Act. From that time on bookmakers largely took to the streets and it became far more difficult for the working man to place a bet*. Ultimately in 1907 street betting was banned as well which resulted in the business going underground until 1961 when betting shops became legal once more.
The 1853 Act was inspired by the anti-gambling lobby. The lobby proposed that for those at the bottom of life's pile, gambling led to debt, crime, prison and the breakdown of family life.
*Private clubs such as Tattersalls remained unaffected on the basis that the rich and titled were capable of looking after themselves (a lot of them weren't).