Basically the “cookie consent” part in the EU stems from the e-privacy directive. Article 5.3 refers to GDPR (through the directive that is replaced by GDPR) and reads:
Member States shall ensure that the storing of information, or the gaining of access to information already stored, in the terminal equipment of a subscriber or user is only allowed on condition that the subscriber or user concerned has given his or her consent, having been provided with clear and comprehensive information, in accordance with Directive 95/46/EC, inter alia, about the purposes of the processing. This shall not prevent any technical storage or access for the sole purpose of carrying out the transmission of a communication over an electronic communications network, or as strictly necessary in order for the provider of an information society service explicitly requested by the subscriber or user to provide the service.
In short, this method may fall under the EU “cookie law” above. The use of timestamps may require consent if they are used to distinguish users (even if only for counting purposes). The timestamps may then also be personal data under the GDPR.