Rachel Reeves has been criticised over a “missed opportunity” to raise £900m from online casinos in her first budget as chancellor, amid concerns about the Labour party’s ties to the £11bn-a-year gambling sector.

Both the Liberal Democrats and Derek Webb – one of Labour’s largest donors – questioned the chancellor’s rejection of proposals to double remote gaming duty (RGD), levied on online games of chance, from 21% to 42%.

The policy, initially proposed by the Social Market Foundation (SMF) thinktank, was among measures under consideration by Treasury officials. It also had support from the Liberal Democrats, who wanted to use the money raised – estimated at up to £900m – to fund health and social care.

But Labour, which has previously faced scrutiny over longstanding financial and personal ties to the gambling industry, ultimately decided not to include the sector among £40bn of tax increases that included a change of policy on family farms and employer national insurance contributions.

The UK’s 21% rate of tax on online gaming will remain below that levied in multiple European countries, as well as states in the US, Australia and Canada.

The Liberal Democrats’ Treasury spokesperson, Daisy Cooper, said the omission “raises serious questions for the Labour government about why they failed to act on this issue.

“It’s particularly worrying that the chancellor is targeting family farms, GPs, hospices and small businesses while letting the big gambling companies off the hook.”

The Lib Dem leader, Ed Davey, had earlier said a duty rise was an obvious choice for a government “who wants to tackle our social problems”.

Reeves also came under fire from the leading Labour donor Derek Webb, a former casino game inventor who now backs campaigns calling for tougher regulation and taxation of gambling.

Webb, who is Labour’s fifth-largest backer and also donates to the SMF, said: “I’m disappointed there’s been another missed opportunity to constrain the greed of the online gambling sector.

“It’s also a missed chance … to win popularity with the wider public, rather than with narrow detrimental business interests,” he said, a reference to a pre-budget poll that showed broad support for increasing gambling taxes.

The government has said gambling taxes, including RGD, will be reviewed with a view to simplifying them.

But sources among those campaigning for higher RGD highlighted that Labour and Reeves have ties to the £11bn-a-year gambling sector.

The Coates family behind Bet365 have donated hundreds of thousands of pounds to Labour and to Keir Starmer’s party leadership campaign.

Rachel Reeves’s constituency office accepted a combined £30,000 from Richard Flint, a former chief executive of Leeds-based Sky Betting & Gaming, and Neil Goulden, then a director of Gamesys, the owner of Virgin Games and Rainbow Riches Casino.

The chancellor has also previously written of a friendship, stretching back to their teenage years, with Michael Dugher, the former Labour MP who now chairs the gambling industry lobby group, the Betting & Gaming Council (BGC).

Grainne Hurst, the chief executive of the BGC, said: “We have been clear: any duty rises now would have hit customers, prevented growth, risked jobs and bolstered the unsafe, unregulated gambling black market.

“Government has listened to the BGC and our members, got the balance right and rejected calls from anti-gambling prohibitionists,” said Hurst, a former Ladbrokes executive.

A Treasury spokesperson said: “The government will consult next year on reforming the tax treatment of remote gambling by moving to a single remote gambling duty, aiming to close loopholes, simplify and future-proof the current system.”