The BHA believes more than a third of the money it estimates could be lost to the sport as a result of a cut in FOBT stakes could be offset by foreign racing after the government revealed it may look at extending the levy to bets placed in Britain on global racing.
According to BHA figures the government's decision to reduce maximum stakes on betting machines to £2 could cost the sport £40-60 million a year once they are fully implemented over the next two to three years.
However after culture secretary Matthew Hancock asked his officials to explore with racing how a levy on global racing bets could work, BHA chief executive Nick Rust said it could net £15-20 million as it will also cover bets on Irish racing.
"Irish racing generates revenue from British racing in that betting in Ireland by Irish citizens on British racing attracts funding directly for Irish racing," said Rust. "That is not reciprocated with our current arrangements in the UK. That would be one of the biggest sources of increasing levy revenue if it was applied.
"We think that could be £15 million, maybe be as much as £20 million. If that was implemented and that was the only measure then that goes some way towards halving the expected impact in two to three years time.
"We are interested to talk to the government about some other ideas about how they would help us to support our sport and the rural economies that we participate in."
The possibility of a return to a levy based on bookmaker turnover from a tax on gross profits has featured among discussions, but Rust said it was "too early to say" whether it would be taken further. He said it would be down to rights holders to decide whether to lower the cost of media rights to help bookmakers keep shops open.
Rust said there was merit in pursuing a minimum margin on online bets from betting operators who offer incentives around big racing festivals to attract new customers.
"A pure turnover levy would be inconsistent with policy elsewhere," he said. "But we would say there may be a case for saying that there should be a minimum margin in place for betting online.
"Because we only get paid on gross profit, if margin is given away on the horserace betting product and the customers bet on other areas and we don't receive that then perhaps there is a case for looking at a minimum margin in those circumstances."
Rust said the government had "got it right in taking action to ensure that measures are in place to protect problem gamblers. There is quite clearly evidence of harm and public concern and cross party support for taking action."
But he said he was "pretty confident" the health of the sport would not suffer as a consequence in at least the short term.
"We've got mitigation promised by government and the secretary of state has instructed us to look at a levy on foreign racing which is in line with other jurisdictions," he said.
"We are committed to a 2018 fixture and funding round which won't be affected. The levy board receipts are healthy. There is no need to rush into action immediately. We are going to need to see how this settles down.
"We made an announcement two weeks ago about the 2019 fixture list and associated funding and at this stage there are no plans to amend that. The announcement was made in the knowledge and anticipation a strong degree of action would be taken on FOBTs and the sport is on the up.
"There are many good indicators, the £40-60 million impact will be two to three years away. There is some mitigation coming in the meantime and I would sincerely hope racing can continue its investment in the future as it has been doing in the last 18 months.
"We may need to adjust moving forward, but given the underlying trends in betting on the sport, in terms of the numbers of horses in training, and the support from government at the moment, I am pretty confident that we will be able to remain in good health over the next few years."