The proposed crackdowns were announced in a long-awaited White Paper on gambling, published yesterday.
It marks the biggest shake-up of regulation in the sector for nearly 20 years.
The Government says online slot machines are a particularly high-risk product.
Its review proposes a consultation on stake limits of between £2 and £15 per spin.
But it also suggests lower limits of £2 or £4 a spin for younger gamblers aged 18 to 24, who it says “may be particularly vulnerable”.
The checks on gamblers would kick in when someone loses £1,000 in 24 hours or £2,000 over 90 days.
Culture Secretary Lucy Frazer told Parliament, the government will also ensure children “can do no forms of gambling”.
It plans to strengthen licensing laws to stop kids from playing slot machines in pubs and aims to ban under-18s from buying any lottery tickets.
The betting industry now makes two-thirds of its revenue from online gambling. Ms Frazer said the rise of smartphones means “now there’s a Las Vegas on every phone”.
Another proposal is a levy on gambling firms in order to pay for addiction treatment.
Ladbrokes owner Entain said it has already implemented a number of actions.
Flutter, which owns Paddy Power, SkyBet and Betfair, welcomed the White Paper.
Sir Iain Duncan Smith, vice chair of the All Party Parliamentary Group on Gambling Related Harm, also welcomed it but said it did not go “far enough on children”.
But fellow Tory Philip Davies criticized the affordability check plans and asked: “Do the punters themselves get any say at all over how they can afford to spend their own hard-earned money?”
And Louise Davies, of charity CARE, said: “There is no need for further consultation…We need legislation.”