Silk, I'm not sure what the Beeb use either, but certainly looks like vector.

If you've money to spend, take a look at Adobe Illustrator. If not, download Inkscape for free at inkscape.org. Also, have you had a look at Open Street Map (www.openstreetmap.org)? You can export data from there in SVG, which is Inkscape's native format. This allows you to import Open Street Map's data directly into Inkscape to manipulate as you please. I haven't a whole lot of experience with this, as I'm more into fantasy mapping, rather than real world, but I'm sure there are lots of tutorials on the web. Of course, other guild members might have more useful suggestions for you, but hopefully this can be a starting point.