This site is a small set of static pages. There is no account to create, no newsletter, no comment form and no login, so there is nothing here that asks you for your name, address or payment details.
What does get collected is ordinary web analytics: which pages were viewed, roughly where in the world the request came from, which site or search engine referred you, and what browser and device type you used. That is aggregate traffic data and it is not used to build a profile of you as an individual.
When you click an operator link, that operator's own tracking is what identifies the visit as having come from this site so any commission can be attributed. Those cookies are set by the operator on the operator's domain, under the operator's privacy policy, and this site cannot read them.
That is the honest shape of it: the commercial tracking on an affiliate page largely belongs to the companies being linked to rather than to the page itself. If you would rather not carry it, most browsers let you block third-party cookies, and a private window discards them when you close it.
Under UK GDPR and the Data Protection Act 2018 you can ask what personal data is held about you, ask for it to be corrected or erased, object to processing, and complain to the Information Commissioner's Office. Because this site holds no accounts, the honest answer to a request will usually be that there is no personal data to return beyond aggregate analytics.
Analytics data is retained in aggregate and email correspondence is kept only as long as needed to deal with the matter raised. To ask anything about data, email info@nongamstopcasinosuk.com.