I have been through a very unpleasant history in the past, none of which was my fault (if you want to take my word for it), and in the end I came out clean without any criminal record.
What happened was I had a bad break up with my ex-partner. She falsely accused me of rape and I was arrested and released on bail. We then tried to get back together, after she had a change of heart, and after awhile I was arrested again "on suspicion of witness intimidation", and released on bail again. We then tried to get back together again, and she has sent a letter to the police withdrawing her previous allegations. Once the police explained to her that she will be arrested for providing false information and wasting police resources, she turned around and claimed I have made her do it under duress. This time I was charged for "perverting the course of justice" and this time no longer released on bail. I was remanded in custody for 10 weeks, and then released on bail, awaiting for the trial. On trial, I was completely acquitted by the Not Guilty verdict. I know what I have done was very stupid (i.e. trying to get back together several times), but after being in prison I did not make same mistake and never contacted her again.
So, technically, I don't have any criminal record. I also think I do not have any pending prosecutions. My only charge was aready settled in a trial. However, when my my solicitor emailed the police to confirm the status with regards to the other allegations, they replied something vague along the lines of "...we reserve the right to bring charges at any time in the future, if any new information comes to light" etc. I am now absolutely certain that nothing will ever come out of it, because that happened quite a few years ago and I have not contacted my ex since and never indend to.
However, I am worried about answering this question on the application form:
"Have you ever engaged in any other activities which might indicate that you may not be
considered a person of good character?"
Have I engaged in the things I was accused of? The answer is NO.
However, the guidance notes say:
You must say whether you have been involved in anything which might indicate that you are not of good character. You must give information about any of these activities no matter how long ago it was. Checks will be made in all cases and your application may fail and your fee will not be fully refunded if you make an untruthful declaration. If you are in any doubt about whether you have done something or it has been alleged that you have done something which might lead us to think that you are not of good character you should say so.
Here, the answer might be YES, in the sense that I was involved in this story, which might indicate to an outside observer that I am not of good character.
Further, Good Character notes from here say this:

Which sounds like the HO could have the discretion to refuse an application, even if a person is not found guilty in the criminal justice system.
I am unsure whether to mention this story at all or not in the application, if doing so might be unnecessary and asking for trouble. The answer to the question "Have you ever engaged in" is definitely NO and it is the true answer. By this logic, there would be nothing to declare. Do you think that's right?
Would be grateful for any advice!