I've had brain fog/presumed CFS for a number of years now. Had the same experience as you - bloodwork clean, after that the NHS did not want to know. Some notes from my experience which may help:
1) Do push for further testing! See different GPs etc until you are sure they will not help you any longer/feel there is not cause for concern. As much as I love the NHS, it unfortunately does come to this a lot. I had to see 7 different GPs to get a vaguely correct Dx on my elbow pain, let alone a symptom such as brain fog. Also as above, try and get a thyroid test, especially if you are having other symptoms. My thyroid is borderline low. I do wonder if that is related.
2) There seems to be a psychological component in that brain fog (and also CFS) can be kind of self-amplifying the more you worry about it. If I force myself to read books, do revision etc, the fog is nowhere near as bad as if I'm doing nothing (or back when I was worrying about it). Same with CFS, if I get out and go to the gym, I am less exhausted than if I just lay in bed all day being tired. Friends with similar condition have had a similar experience.
3) As others have said, there can be a number of different causes. Depression and anxiety seem to be a common factor too, and those things certainly aggrevated it for me.
edit~4) It has improved, over time, for me. So there is hope.