The sports minister Tracey Crouch resigned because she believed pro-gambling MP Philip Davies successfully went above her head to secure a delay to curbs on fixed-odds betting terminals (FOBTs), defying her on a policy she had overseen.

Friends of Crouch said she was “furious” after discovering that the digital, culture, media and sport secretary, Jeremy Wright, discussed gambling regulation with Davies during a private meeting.

Crouch had pushed for the maximum stake on FOBTs, described by the government as a “social blight” earlier this year, to be reduced from £100 to £2 from April 2019.

The date was understood to have been included in a draft version of the chancellor’s budget, before being changed at the last minute to October.

Political allies of the sports minister, who launched the FOBT review in 2016, said she believed Davies was instrumental in persuading Wright to choose the October date, allowing bookies to make an extra £900m from the machines.

In her resignation letter, Crouch branded the delay to FOBT reform “unjustifiable”, adding that it was the result of “commitments made by others to those with registered interests”.

The comment is understood to be a reference to Davies, a frequent recipient of gambling companies’ generosity according to the parliamentary register of members’ financial interests.

The Tory MP for Shipley has enjoyed hospitality worth £3,204.44 from bookmakers and betting companies including Ladbrokes, William Hill and SkyBet in the past year alone.

Davies did not return requests for comment from the Guardian on Friday. But asked about his involvement on Thursday night he said: “I have never known that I have ever been single-handedly responsible for changing government policy but obviously you would like that to be the case irrespective of how unlikely that sounds. I only wish I had such sway over government policy.”

The former sports minister Tracey Crouch had pushed for the maximum stake on FOBTs to be reduced to £2 from April next year. Photograph: Stephen Pond/Getty Images for Sport England

Wright, speaking in the House of Commons earlier this week, indicated that he had brought forward FOBT curbs, which he said were initially due to take effect in April 2020.

“I have heard language twisted to various uses in this place, but the idea that a move from April 2020 to October 2019 is a delay is going a little far,” he said.

But the Treasury repeatedly denied it had set a date when it was first reported in June that 2020 was under consideration.

Davies also denied a suggestion from multiple Whitehall sources that he told Tory whips that if he did not get his way on FOBTs, he would vote with Labour if it revived proposals for a fresh inquiry into the activities of the press, nicknamed Leveson 2.

“There’s been no quid pro quo, it’s offensive beyond belief to suggest that I’m going to vote for something I fundamentally disagree with and it is categorically, 100% untrue,” he told the Yorkshire Post.

“I have never even spoken to Jeremy Wright about Leveson 2. It may be that there’s been quite a few other Conservative MPs who have been attempting to blackmail the government over this issue but I am certainly not one of them.

“I haven’t said that I will vote against the government on x, y or z if they don’t do this that or the other. I have absolutely not done that at all.”

Crouch and Davies have clashed before, according to the Labour MP Graham Jones, who tweeted in May that he had seen Davies “verbally attacking” the sports minister in the House of Commons tea room. One source familiar with the exchange confirmed that it was about gambling regulation and that Crouch had “given as good as she got”.

The government, in addition to pressure caused by Crouch’s resignation, is now facing the rare prospect of being forced to change the budget.

A cross-party group of MPs, including more than 30 Tory rebels led by the former party leader Iain Duncan Smith, are expected to put their names to an amendment to the finance bill, which – once enacted – implements the budget.