In Canada and the US you will need to remove this contact from your mailing lists in 10 days. In the EU and UK, this time limit is 30 days.
USA & Canada
The US CAN-SPAM law and Canada’s CASL require that companies remove any individuals contact details from their mailing lists within 10 days or receiving an unsubscribe from them.
EU & UK
EU GDPR and UK GDPR require that any data subject access request, e.g. unsubscribe, opt-out or objection to processing, must be actioned within 30 days of receiving the request.
If the request is especially complex the 30 day timeframe can be extended by two further months. However, within the first 30 days the company must acknowledge receiving the request, confirm or clarify what is being requested, and decide whether they can act on the request. If they decide not to action the request (extremely rare that this scenario would ever be applicable), they must inform the individual of this and advise them on their right to lodge a compliant with a Supervisory Authority.
Disclaimer: The contents of this article are for informational purposes only, and not for the purpose of providing legal advice. You should contact your legal counsel to obtain advice with respect to any particular issues or problems.