Current Region:

In some cases, yes.

While the ICO lists a number of options to provide age-assurance, the responsibility lies with the website to adopt a suitably robust approach dependent on the level of potential harm the site may cause if children too young to use it are given access.  In fact, this is already the law in the UK, under the Data Protection Act 2018, but the AADC will bring greater focus on this aspect of that law.