The cookie law is part of the ePrivacy Directive (or PECR in the UK) rules that have been in place for many years. The infamous cookie law is only part of the regulation.
The GDPR is a new set of rules in addition to, rather than replacing ePrivacy (or PECR in the UK). In fact, the ePrivacy Directive is getting an upgrade in 2018 (update: this date has been pushed out to 2019) so be ready for this!
If you haven’t brushed up on the ePrivacy Directive in a while, then it’s time to do it now.