Hi sibbooks and welcome to the forum,
Yes, you are right that copyright does not protect concepts and ideas. It is an individual's expression of the idea which attracts the protection. There can sometimes be a grey area where the idea and the expression overlap, when it is a matter of establishing whether a substantial part of the first work has been used in the second work. But provided that the planned structure, and the 10% of your book which you have already written, was done without even knowing of the existence of the other book, it is unlikely that it will have been an unconscious influence.
As this is non-fiction work, if you feel that the other book contains material which you would also like to cover, you can do this by openly quoting small passages from the first book, as long as you cite your source, for instance in a footnote. This is permissible using an exception to copyright contained in
section 30 of the Copyright Designs and Patents Act 1988. Each extract should be only as long as is necessary to convey the point you wish to highlight, and no more. This saves you having to elaborately paraphrase something you want to say and you know that the other author has already written about it.
There have been a number of court cases over the decades which have shaped the way that the law of copyright should be applied when a court needs to assess the degree to which the expression of one author has been copied by a second work dealing with the same or similar topic. The best known is probably one in which two authors, Michael Baigent and Richard Leigh, alleged that Dan Brown had infringied their copyright, in his book
The Da Vinci Code. They lost at first instance and appealed, but also lost the appeal.
If you would like to see how the evaluative process typically operates, you can read the two judgments here:
First Trial
Court of appeal