Increasing taxes on betting firms in the Budget has been suggested to the chancellor. She recently told ITV: "I do think there is a case for gambling firms paying more... they should pay their fair share of taxes and we will make sure that happens."
Reeves has been encouraged by former Prime Minister Gordon Brown to increase taxes on the gambling sector and use the revenue from that to reduce child poverty.
The Institute for Public Policy Research (IPPR) think tank estimated over the summer that additional taxes on the industry, as high as 50%, could raise £3.2bn.
At the time the Betting and Gaming Council, which represents gambling companies, called Brown's plan "economically reckless", saying it would push gamblers into the black market.
Betting companies have resisted calls for taxes to rise. Up to 200 William Hill retail outlets could close if the industry faces higher taxes, its owner Evoke said earlier this month.
Betfred's Mr Done said that if taxes on UK gambling companies increased he would also feel compelled to close his High Street shops.
"It [tax] doesn't even need to go up to 50%. If it went up to anywhere like 40% or even 35% there is no profit in the business. We would have to close it down. I'm talking job losses. We're talking probably 7,500," he said.
He said 300 of his shops were "currently losing money" and claimed a 5% increase on gambling taxes would raise that number to 430.
"Once the [UK] industry is closed down, it's gone. People will still bet, but they'll bet offshore with it. There's plenty of bookmakers offshore who happen to take the bets, who don't pay anything to this country," he said.
Punters' winnings from gambling are not taxed in the UK, nor is VAT charged on bets. However, the gambling industry pays extra taxes, including:
* a tax of 21% on online casino gaming stakes
* duty of 20% on slots and gaming machines
* general betting duty on sports fixtures of 15%
* general betting duty on horseracing of 25%
Mr Done said recent increases in employer National Insurance Contributions (NICs) and the minimum wage had already added £20m to his company's costs.
He agreed that, like with banking or buying clothes, customers are increasingly going online, making it inevitable to close betting shops.
Rival firm Paddy Power on Thursday said it would close 57 shops across the UK and Republic of Ireland, citing increasing cost pressures and challenging market conditions.
"Slowly it will go online, but we're talking, without tax increases, we've still got probably 20 years of life on the High Street," said Mr Done.
"And you know, the UK High Street is being decimated with closures."
In its most recent annual results, Betfred took in nearly £1bn of revenue, but made an operating profit of just £500,000 after a series of writedowns on its assets.
The family-owned company has bases in the UK, Gibraltar, the US and South Africa, with investment in both online gambling and High Street sports betting.