This OW RTW video says that it's cheapest for the start city to be Oslo or Budapest. But then how it is possible to get the RTW booking tool to list Oslo (or any none OW hub, but which OW flights are from)? It's happy to start at a OW hub, e.g. it lists London. I have a RTW route in mind and I'm 99% certain the OW RTW tool will not build it: OSL-MAD-PVG-SIN-AKL-EZE-UIO-OSL, as AKL-EZE will only work with SYD-SCL and there are no intra-South America OW members.
Well you can build it and then you see the price. I think Matt did a good summary and give many reason why to avoid some airlines (such as QF long hauls) and avoid some airport (such as London). But you can start in London or any other OW hub. You will have to pay more than from OSL or BUD.