All I can tell you from my experience is that it varies. Examples:
1. LHR-ICN (Seoul Incheon) with BA back in 2013: outbound upgrade from economy to premium economy (WT to WT+ is BA-speak) was about £200. For the return trip, the same upgrade was around £100. I asked about this one at the airports.
2. Again in 2013, LHR-WAW (Warsaw) outbound economy to business upgrade was £79. For the return trip it was only £6 (six) pounds. That one I went for. It was worth it just for the "free" drinks in the lounge beforehand, even though the lounge in Warsaw airport is nothing special. These upgrades were through the BA web site.
I have heard other examples of really cheap short-haul upgrades, for example someone doing LHR-Gibraltar got an economy to business upgrade for £14. That was a number of years ago however.
Last edited by chrissw; 15th February 2016 at 15:37.
Reason: Grammar correction