Turkmen prior to COVID and then being banned from airspace served both LHR and BHX and did so for many years starting off with 737, then 757 and 777 (the latter only occasionally seen at BHX). The BHX service was 4 X weekly and had very high LF's. The reason: they operated ASB-ATQ and DEL which filled the flights from BHX
I can't speak for LHR but AI arrived at BHX and have seemingly mopped up on the BHX-ATQ and DEL routes since resuming flights post COVID, although they both co-existed at BHX happily enough before 2020.
T5 don't fly onward to either ATQ or DEL anymore hence the lack of pax from STN and I assume now LHR. BHX without a connection to ATQ will never return and even if it did, AI are now dominant on the route.
A 1 X weekly LHR service is but a shadow of what they operated to/from the UK prior to 2020.