Many such critical business services, such as Mastercard and Visa, have previously indicated they would not choose to provide their services to websites in countries where a national regulator found them to be non-compliant with the law. There is a reputational risk to their brand if they continue to do so.
Well-drafted laws, such as the UK Online Safety Act can give regulators (in that case, Ofcom) powers to require search engines, payment, advertising and hosting services etc. to withdraw their services to non-compliant sites.
Regulators often also have the power to ask Internet Service Providers (ISPs) to block illegal sites, as they already do regularly to prevent access to Child Sexual Abuse Materials, terrorist content etc.