Earlier quoted context omitted.
No, the enforcement is through the national "supervisory authorities" such as the ICO. Most of the enforcement process is through national courts and the ECJ is only for the final layer of appeal. This very article says "German Court rules ..." > voided the UK's opt out of new human rights related legislation, despite a very clear paragraph in the treaties saying they did not apply to the UK. [citation needed]; did y…
See here: https://fullfact.org/europe/eu-and-human-rights/ In the section "Wasn’t the UK supposed to get an opt-out from EU human rights laws?" The summary is, when the Treaty of Lisbon awarded the EU new human rights powers the UK and Poland negotiated an opt out which was written in the treaty. It was a part of convincing the UK government to accept the new treaty without granting a referendum on it, as they had pr…
> This Charter reaffirms [...] the rights as they result, in particular, from [various pre-existing sources].
The opt-out specifies that the Charter does not _extend_ the ability of the courts, but does not limit the powers that the ECJ already had prior to the implementation of the Charter. Even if the UK had a cast-iron opt-out (e.g. "The Charter, in its entirety, is not applicable to the UK, no rights are granted under it to UK citizens, and no court may refer to it in reaching a decision affecting the UK"), more or less the same results would likely be reached.
Also note Article 51(2): "The Charter does not extend the field of application of Union law beyond the powers of the Union or establish any new power or task for the Union, or modify powers and tasks as defined in the Treaties.". This is broadly similar to the UK/Polish opt-out, further suggesting that the Charter did not grant powers that the UK had not otherwise agreed to.
> In other words, this part of the treaty does not allow the courts to overturn UK laws. Stated twice, for clarity.
It does not grant them _new_ abilities to do so, and the second statement only refers to a subset of the rights considered under the Charter.
http://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX:120...