The ABRSM exam syllabus, and the set pieces for each grade, will certainly work as a logical progression. ABRSM also publish other "graded" collections of pieces.
However these ABRSM publications don't include any teaching material, though you can find YouTube videos created by qualified teachers to provide some of that.
It is probably worth supplementing the ABRSM books with material which has its primary aim of teaching. There are several series of "adult piano course" books available - Alfred, Bastien and John Thompson are three well known ones.
The best way is undoubtedly to get a teacher, who can see when you are doing something wrong and correct it before it turns into a bad habit - but if you can't use a teacher for whatever reason, that's no reason not to try to learn without one!
If the problem is simply the lack of a teacher where you are living, you may be able to find somebody who gives "remote lessons" via Skype, etc. That is certainly being done for advanced music tuition, but I don't know how common it is at beginner level.