The problem at Uralsk is not runway length or width, it is PCN. The PCN of the runway is only 20, which is very light indeed and precludes operations by many types of aircraft. It is not an uncommon problem in former Soviet airfields where Russian aircraft tended to have lots of wheels across which to spread the weight of the aircraft, thus reducing the weight footprint of each wheel on the tarmac.
The only European carrier flying there is Astraeus which operates a weekly 757 flight to service a nearby major oil & gas facility. The 757 is OK for ops on this runway due four-wheel main gear bogies. I would imagine that BA would have needed a dispensation to operate A320 / A321 equipment in there from the airport authority and their flight ops people as it is definitely above the ACN which can be supported by the PCN of Uralsk's runway.
The other factor is that the runway is probably one of the bumpiest in living memory - surface (particularly at one end, I think 04) is quite poor.
I can imagine that a 747-400 landing here would create an absolutely huge stir.