Just asked my other half, who is actually from Islamabad.
He could think of a couple of reasons why BA specifically fly to Islamabad.
First of all, there are a lot of expats there and Rawalpindi - more than anywhere else in Pakistan - and there are a lot of NGOs. Apparently Pakistani expats living in Britain don't generally tend to fly BA because Halal food isn't as prevalent, and PIA do things like have an entire channel which contains nothing but Koranic verses.
Apparently the UN also fly one flight a day from Islamabad to Kabul; my other half surmised that BA might provide some feeder traffic to this.