I can't believe the guff this Government comes out with, and I actually heard a senior member of staff at my last University perpetuate this myth.
I am living proof by experience that CSEs (or maths, at least) were every bit as difficult as 'O' Levels, and actually more difficult in the case of mathematics.
The main difference between the two in the marking system; to get a CSE equivalent to an 'O'Level, you had to get a grade one; the coursework, however, was just as challenging.
CSEs meant that people who were unlikely to pass an 'O' Level could gain a qualification in that particular subject that showed they had done a course of study.
When I were a nipper, McMum and McDad were told by my school that I was too thick to pass 'O' Level maths, so they paid for private tuition so that I could do CSE maths as well. It was a different course focused on a different style of maths, so I had to do two different syllabi.
I preferred the 'O' Level one because I liked geometry (0% in the mock exam) and algebra (8%), though I hated triganometry because nobody would tell me what it was for.
CSE maths had all sorts of other types of maths (slide rules etc) which I found even harder than the 'O' Level course although my teacher was much, much better.
I ended up passing both, but I can state categorically that CSEs were difficult exams.
I also do not believe that exams have been dumbed down, having seen what both daughters had to learn for both GCSE and 'A' Level exams.
Know what? I believe the unsayable: state education is better than it has ever been. Young people are better informed, better taught and generally much more able than they used to be.