The main chart in the link is for Low Level Airways. The CTL frequencies are primarily for access to airways and the TMA (same as London Control).
The smaller FIS chart (which I have never spotted before, tucked in the corner) would be very useful, as you say, if it did not group the sectors together. In reality, you could dial in the first frequency in the list and if it was wrong the controller would just say "please call my colleague on xxx.xxx" or "call me back on xxx.xxx" if band-boxed.
There is a more descriptive text version of the FIS sectors in the AIP, but an associated chart would certainly help.
Edit to add a link to the definitive but not user friendly
FS Sector list