Sports minister Tracey Crouch has resigned over the government's delay in bringing down the maximum stakes for fixed-odds betting machines.

In his budget earlier this week, chancellor Philip Hammond announced the cut in stakes – from £100 to £2 – would not come into force until October 2019.

Many MPs, including those on Labour benches, said they were led to believe the new limit was going to be introduced in April 2019 – while the government insists the original plan was to cut it in April 2020.

Crouch, who was hoping for confirmation of an earlier date, said pushing back the issue was "unjustifiable" and it could "cost the lives of problem gamblers".

In an open letter of resignation to Prime Minister Theresa May, Crouch wrote: "Your personal support earlier this year for a reduction in the stake of fixed odds betting terminals incredibly welcome.

"I cannot begin to explain how many people got in touch to congratulate the government on its stance, including addicts, their families and, also, sadly, those who have been left behind after loved ones took their own lives as a consequence of addiction.

"Unfortunately, implementation of these changes are now being delayed until October 2019 due to commitments made by others to those with registered interest.

"From the time of the announcement to reduce stakes and its implementation, more than £1.6bn will be lost on these machines, a significant amount of which will be in our most deprived areas – including my own constituency."

"In addition, two people will tragically take their lives every day due to gambling-related problems and, for that reason, as much as any other, I believe this delay is unjustifiable."

Crouch was first appointed sports minister in May 2015. A self-confessed “sports nut”, she has been MP for Chatham and Aylesford in Kent since 2010 and first became a member of the Culture, Media and Sport (DCMS) Select Committee in 2012.

Seen as a genuine advocate for sport, Crouch first hit the headlines in 2011 when she criticised the Football Association and its laws on mixed-gender games, which prevented her from playing for the Parliamentary football team.

In January this year, she was also appointed to the newly created position as minister for loneliness, a role she shared with her DCMS responsibilities.