The government is to cut the maximum stake on fixed-odds betting terminals (FOBTs) from 100 pounds ($130) to just two pounds, but announced this week the reduction would not take effect until next October.
The move came after ministers opted to try to tackle problem gambling on the machines and rejected claims that such a big reduction could cost thousands of jobs.
The reduction had been announced by Crouch, 43. The BBC said she had expected the change would be brought in from next April.
She tweeted her resignation letter to Prime Minister Theresa May, in which she said: “It is with great sadness I have resigned from one of the best jobs in Government. I believe this delay is unjustifiable.”
In a letter to Crouch, May said there had been no delay.
“Indeed as you know from your work as the minister responsible, we listened to those who wanted it to come into effect sooner than April 2020 and have agreed that the change should take place within the year - by October 2019,” May wrote.