Qatar A320s used to operate from Heathrow to Doha
I think you'll find that was a Business Class-only 319 (no longer operating), but you're point is well-made as Qatar (and another MEB3 airline I can't mention on here) use their 320's on some fairly long sectors from DOH and AUH. Gulf-Air also run 320's to BAH from LHR on a regular basis.