Notes: I'm using ECHR for the European Convention on Human Rights, and ECtHR for the European Court of Human Rights, which adjudicates said Convention. Also, I assume the UK Human Rights Act 1998 (HRA) would be repealed as part of ECHR withdrawal, an Act it passed as part of its commitment in the Belfast Agreement.
There are four scenarios which I think are distinct:
- ECtHR judgments against the UK: The UK government is only bound by the ECtHR because it has agreed to it as part of its membership of ECHR. Leaving the ECHR means ECtHR case law is no longer binding on the UK government. Note I specifically said "government." The ECHR is a treaty which governments agreed to. The ECtHR is not formally an appeals court and was never directly binding on domestic UK courts. Instead, a negative ECtHR judgment is meant as a trigger for domestic legislative change.
- Domestic UK court finding legislative ECHR violation: This never produced binding case law. Instead, UK courts issue a declaration of incompatibility as per the HRA. Again, this is a trigger for domestic legislative change and produces no actionable immediate effect.
- Domestic UK court finding regulatory ECHR violation: Unlike Acts of Parliament, domestic UK courts are empowered by HRA s. 6 to remedy ECHR violations by public authorities, so long as these were not a result of following parliamentary legislation. This is the scenario the Miller case you cite falls into. On repeal of the HRA, nothing would immediately happen, but if similar cases arise to previous ones relying on the HRA, they would likely have to be newly adjudicated. This isn't peculiar to the ECHR, this is just what happens when legislation changes, and indeed part of the point of changing legislation.
- Domestic UK court interpreting legislation and regulations in accordance with the ECHR: This is the least clear scenario, and will highly depend on how the UK might opt to leave the ECHR. HRA s. 3 requires UK courts to interpret legislation and regulations in accordance with the ECHR whenever possible. They could leave old case law intact by specifying that past legislation was enacted with ECHR in mind, and so should continue with that interpretation. Conversely, this scenario could just get folded into Scenario 3, with past precedent no longer binding due to legislative change. A middle ground could also be sought as with Brexit: EU case law is treated as binding precedent, but the Supreme Court (and Scotland's High Court) are explicitly allowed to overturn the precedent, while lower courts cannot (European Union (Withdrawal) Act 2018 s. 6).
So in summary, while I'm sure leaving the ECHR would cause quite the political change, from a legal perspective, it's fairly straightforward. Scenarios 1 & 2 I mention above produces no practical legal change, while in Scenario 3, and to a lesser extent Scenario 4, there's not too much different from any other legislative change.