The extent to which ECHR and CoE membership are sovereignty issues is, to put it mildly, debatable. Turkey and Russia are members. It’s hardly conceivable that either of them would be so if they believed their sovereignty to be affected!
When you have the ECHR issuing rulings saying that (criminal) prisoners should have the right to vote, that is a sovereignty issue. Parliament hasn't given effect to the ruling so it's of limited influence, but it's still a sovereignty issue.
Personally, I'm not necessarily in favour of Britain withdrawing from the jurisdiction of the ECHR or the CoE. I do agree that its influence is limited and as long as Parliament always retains the power to decide how to give effect to rulings (including whether to give effect to them), it's not a huge deal, but I was mentioning it because a lot of people do think sovereignty has to be absolute to be real and I was just pointing out that even if the UK completely leaves the EU, there are still other treaties in effect that tie it to Europe in other ways.
My problem with the European Union is the concept of 'ever closer union'. At the moment I do believe the UK is still a sovereign nation even within the EU - but I'm not convinced that it would stay that way and so that's why I want it out. If the EU was still the common market that Britain joined, I'd be all for it. If it was guaranteed that it would stay as it is now I could even live with that - that's a personal position, I know many who are more hardline on leaving than I am and I don't want to suggest my position would satisfy most who want to leave.