Polo isn't posh? You're talking about the one on horses? All equestrian sports tend (not tend) to be elitist, therefore considered 'posh' because horse ownership is costly.
As for hockey it's avalible to a huge number of people from all backgrounds but it's not one of the major popular sports such as football. Schools offer a lot a sports but I would hazard a guess in most (note tip say most) it's the boys football team that get the most attention. My school was unusual because we'd just churned out a British team hockey captain who'd played in the olympics.
As for hockey being a white sport you have to consider the attitude towards it as a less popular sport, someone who is from a culture where hockey didn't feature are least likely to consider playing it despite it occurring a few times in PE. Modern field hockey is a very British sport (which was strong amongst public school many years ago (hence the posh label I guess) before it started featuring as standard) and so has a very white background.
So in other words it's simple not a widely popular sport, that has a label of posh; it's remained niche purely because it is niche, and so hasn't enough appeal to any group that it isn't already normal involed in it. This gold medal may change that though, but the 'white posh sport' label needs to be broken first.
Another (probably more so) example of a niche sport is hurling and Gaelic football, not many playing it in Britian outside of those whose family somewhere along the line is associated with Ireland; but there's a good few GAA clubs in Britain but it's not like many outside of its usual demographic consider it.
This all aside the women's British hockey team have achieved a gold medal. They have done brilliantly. They will have achieved this despite it not being a massively funded sport and despite the fact they are women whose sports are mostly overlook. They deserved huge praise regardless of their class or race.