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.