Kevin you are indeed correct. Around 1988/9 there was a sudden expansion of dedicated freight traffic following the introduction of TNT and Fedex. This also attracted the attention of UPS who were far greater in size then. I was present at a meeting with the top brass from UPS who had set out their vision for European expansion based on BHX. Although site constraints were an issue, everyone was positive it would work. However, the Airport Committee rejected it wholesale, particularly with Solihull Council being vehemently opposed. In addition, British Airways, who had invested heavily in a loss making transit shed, also made their usual threats.The rest of course, is history and a continued reflection of the mis-management of this splendid resource.
Yep it seems that the Night Flying policy precludes any serious cargo operations from any of the major parcel carriers these days.
Looking into it BHX is limited to 5% of annual movements or 877 night departures per year (whichever is lower), which is less than 2.5 departures a day.
Interestingly though, BHX is not bound by the DfT to even have a Night Flying policy, it could theoretically operate unlimited night flights, however it seems they agreed to have the policy as a S106 condition for a Planning Permission with Solihull Council ( I assume this was for the runway extension, not sure.)