The Government has U-turned over plans to delay a cut to the maximum stake on Fixed Odds Betting Terminals, after a revolt that saw a minister resign.
More than 70 MPs had tabled amendments to Government business to force it to cut the maximum stake from £100 to £2 in April next year as originally planned.
At the end of October, Chancellor Philip Hammond confirmed that the cut to the stake would be pushed back until October 2019.
The move led to the resignation of Sports Minister Tracey Crouch on November 1.
Gambling can 'devastate lives'
Mrs May was asked at Prime Minister's Questions on Wednesday about the change by former Tory leader Iain Duncan Smith, who co-led the revolt.
He said: "I was enormously proud of my Government for agreeing to lower the stake on fixed-odds betting terminals to £2 because they have caused endless harm, terrible damage to families and it was the right decision.
"Since then, there has been a hiatus about the date at which this would start.
"Can I ask my right honourable friend: is it a reality that now we have put down an amendment, that the Government will accede and we will get this process started on April 1 next year?"
Mrs May replied: "I know he has campaigned on this issue with a passion because, as he said, this question of the maximum stakes for FOBTs is one which does have an impact on vulnerable people as well as their families and loved ones.
"I recognise the strength of feeling on this issue. I know gambling addiction can devastate lives.
"Our priority is making sure that this change delivers the result we all want to see, we are listening to the concerns being raised by colleagues, and if my right honourable friend will have a little patience I can tell him my right honourable friend the Culture Secretary will set out further details later today."
Culture Secretary Jeremy Wright put out a written ministerial statement on Wednesday.
Mrs May’s answer was welcomed by Ms Crouch who described the possible U-turn as “common sense prevailing”.
“I am pleased that common sense has prevailed,” she said.
“I am sorry that my views as the Minister in charge of the policy were not heard, but I am delighted that the collective voice of Parliamentarians, faith leaders, victims of gambling addiction and their families, press and media commentators and many members of the public have been.”