Street self defence is all about dealing with attacks in real situations. Street self defece moves are designed to be effective, easy to learn and apply and basically to get the job done! Many martial arts are based on attacks you just don't encounter on the street. For example, in aikido many of the attacks are based on those samurai would have used on ancient battlefields.
A martial art which can be compared with street self defence is the Russian Systema. There uis much debate on the origin of this martial art but it's palin to see that a huge multi cultural country like Russia would have many different fighting styles. These are fused into what has become Systema. I believe Systema is a truly effective martial art but sadly there are few places that teach it in the West.
Systema has absorbed and combined elements from Chinese martial arts, Japanese martial arts, European martial arts, and even parts of Greco-Roman wrestling. Its moves and techniques are short, sharp and to the point - just like street self defence.
Another martial art which can be compared with street self defence is krav maga. Krav maga is a hand-to-hand combat system developed in Israel that involves wrestling, grappling and striking techniques. It is known for its extremely efficient and brutal counter-attacks and is taught to elite special forces around the world. Again, sadly you will find it hard to find somewhere to learn krav maga in most parts of the world.
Mixed Martial Arts (MMA) is of course another martial art we can compare with street self defence. MMA fighters vary wildly in their range of techniques and styles but ultimatly its all about getting the job done!
The beauty of street self defence is that the moves can be learnt from books and DVD's. Yes it best to find somewhere which teaches it but you can certainly get a good grounding learning it yourself.