I'm not a laywer, but here's my view of the legal situation you are in.
Accessing protected data without permission is a legal offense in most countries. This includes using a login data you'd expect not to work. It doesn't matter if you try a single password you know or guessed, or brute-force using an online password list.
Therefore, admitting you have accessed such data theoretically exposes you to legal action. It doesn't mean you will be found guilty: in fact, I would expect a reasonable judge to understand your motives (which are clearly to help your old employer, not to harm them) and dismiss the case, but you'd still have all the legal trouble. Moreover, your old employer will have nothing to gain from such actions: they can only demand compensation if they prove the damage you've done, which will be next to impossible since you didn't do anything with the data.
Sending a registered letter demanding to remove your access will not fully protect you. If they suspect you did access the data, they will easily find your login attempt in the logs, and sue you on those grounds, without mentioning your letter. And since the letter will be dated past your login attempt anyway, it will not offer you much protection in court either.
Not telling your old employer you accessed their data is arguably even worse, at it runs the risk that they will find it out on their own. In case of a lawsuit, it will be even harder for you to argue that your motives were benign if it looks like you tried to cover it up. Plus, if they get hacked by someone else and actual harm will be done, you will be on the hook for damages unless you can prove it wasn't you.
So, tell your employer you logged into your old account by mistake and ask them to disable it. You can do it via registered mail if you prefer, but don't expect it to offer much additional protection. I would only do this if they ignored my e-mail, an e-mail answer will be just as usable in court if it comes to this. Don't hire a lawyer until they sue, which they most likely won't as there's no reason for them to do so, as explained above.