(the EU does requires members to be CoE members, and so there were some people suggesting that after leaving the EU the UK might also leave the CoE - possibly including theresa may, I haven't checked - but that doesn't currently seem likely to happen)
The EU Charter of Fundamental Rights is definitely a thing - basically a copy of the ECHR into EU law - but it's only applicable (1) to actions of EU institutions, (2) as a restriction on EU legistation, and (3) as an obligation on member states _when interpreting / implementing EU law_. It has no relevance to UK law other than that. (And what little relevance it would have had to the UK was further weakened since they had a partial opt-out to it that tried to get rid of the last of those for the UK!).
The cases about UK surveillance legislation (eg [0]) were all ECtHR, not CJEU.
[0] https://hudoc.echr.coe.int/app/conversion/pdf/?library=ECHR&...