How many flights per week did/will Turkmenistan serve BHX with? If its a case of fly with Turkmenistan from BHX on particular days that don't suit your itinerary or fly via somewhere on days that do fit your itinerary, most people will do the latter.
There's probably also a matter of 'entitlement' with travellers in the south east. As London is the largest airport system in the world, and Heathrow the busiest in Europe, passengers will likely not look elsewhere for flights, even if they are direct/non-stop. "If there aren't direct flights there from Heathrow or Gatwick, how could there possibly be flights there from any other airport in the UK?"
We're always saying on here that people should fly from BHX even if it means with a stop rather than taking a direct flight from London. It's unrealistic to say the same shouldn't apply to the south east.