I have had some whilst silver on BA long haul- from Y to W, LHR-SIN and a year prior to that from W to J SIN-SYD. Plus a long time ago Y to J SFO-LHR. None so far whilst Gold, but to be fair that's only a few months and I have yet to step on a BA plane in this membership year.
As an alternate data point, when flying CX in PEY, I have had a great many upgrades both intra Asia and to the US (am SIN based these days) when a BA silver for a year, and probably a few more when I held CX gold & then diamond for a while prior to that. I'd say, all in, prior to holding gold with BA, my CX upgrade run was north of 50%.
So random luck on BA I would say, but from experience I would say CX have a more proactive approach.