The call follows warnings from social care leaders that a rise in National Insurance in this week's Budget will force care homes to close.
Davey said: ‘Hundreds of thousands of lives have been devastated by problem gambling – now driven mainly by online casino-style games.
‘This Budget was a missed opportunity to double Remote Gaming Duty, combating the harms of problem gambling while raising money for our NHS and social care. This would have been much fairer than hitting hardworking families, small businesses and family farms.
‘Instead, the Government has kicked the can down the road again. Liberal Democrats will continue to urge ministers to stop dithering and act now, before more lives are ruined.'
Social Market Foundation analysis has found doubling the rate of Remote Gaming Duty would raise between £575m and £900m a year, depending on how much the higher rate reduces online gambling.
Online gambling revenues increased to £6.5bn in 2022-23, according to figures from the Gambling Commission. Around 300,000 adults in Britain experience problem gambling, as well as roughly 40,000 children.
Public Health England has estimated that gambling costs the UK economy around £1.4bn a year, through a combination of financial harms and the impact on physical and mental health, employment, education and crime.
A HM Treasury spokesperson said: ‘The Government will consult next year on reforming the tax treatment of remote gambling, including online gambling, by moving to a single remote gambling duty. This will aim to simplify, future-proof and close loopholes in the system.'