The Freedom of Information Act allows you to get statistics from public bodies.
It defines what are public bodies.
if you then go to the schedules listed, you will find the reference to the various lotteries if you search on this page.
it appears therefore that you are able to get this information under the Act.
Can I clarify anything for you?
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I can only give you the statutory provision which mentions the Lottery although there are several mentions of the organisation and it may be that the particular organisation within the lottery that you need the information from is not the one covered under the legislation. I can’t think for one moment that they would lie in writing.
Other than the Freedom of Information Act, the only way to get this information would be an application to court for pre-action disclosure if you were thinking of litigating. I can’t think why you would litigate but that’s the only way you can get the information otherwise.