So far, the accuracy that is possible is an unknown -- at least, BAE haven't let on as to what they think it will be. GPS accuracy varies with the landscape, too, but at least we have an idea of what to expect.
It's also not likely to be very useful outside of urban areas. I doubt it would help me much in the mountains of Colorado, for example.
Articles on the topic seem a bit schizophrenic. For example, in one BBC News article, it is stated that "The device works by picking up all the available signals nearby, heavily relying on medium wave radio frequencies." At the same time, it is stated that "But mobile phones, radios and TVs use signals that are a lot more powerful than those from navigation satellites, as they are broadcast from only a few kilometres away, and cannot be jammed." Most of those signals are definitely NOT medium wave signals. A system that could successfully pick up and make use of signals over that range of frequencies, separate them based upon location, and use them for triangulation ... well, it would be quite the system, and would necessarily be supported by a whopping big database.
In another article by BAE itself, it notes that "It is also able to work in the most remote parts of the world, such as the Arctic, by picking up signals that include Low-Earth-Orbit satellites and other civilian signals." It sounds like this thing will require a "DC to Daylight" receiver and heaven knows what sort of antenna system to obtain good directional information.
In an 'open' signal area, this service might provide some decent results, but then so will GPS. In an urban landscape, the signal strength overall will be higher, but the received signal strength will still be all over the map as anyone who has done propagation studies in urban areas will tell you. That points us back to accuracy.
For those who point at cell tower triangulation of a phone as an example, it's a LOT easier to perform this magic in reverse -- the cell sites (the receiving end, in that instance) are elevated and in fixed locations.
The best potential use for this technology, if the accuracy can be proven, is in areas where L1/L2 signals cannot penetrate due to signal strength at that frequency. Even then, it's going to take one heck of a database of signal strengths of all kinds of signals vs. location for it to be useful... no doubt the most expensive and extensive propagation mapping service in the world.
I think we need to wait a good while to see a lot of specifics filled in before we assume that this technology is going to ever make it to a consumer unit whose accuracy can be depended upon.