Training martial arts for self-defence is in most cases not a good investment in my opinion. The shock and ferocity of real violence is significant. Unless your training puts you under combat stress triggering fight-or-flight response, your training won't be sufficient to cope with the adrenaline and loss of motor control that real violence will give you.
Also, the sheer amount of effort, money and opportunity cost it takes to learn a martial art to a respectable degree is not a particularly balanced trade-off, especially when the best self-defence techniques are free (exercising caution, keeping your ego in check, knowing when to leave, etc.). Even if you get into 5 fights in your life (and that's a lot for someone trying to stay out of trouble), each fight will probably last for less than 1 minute, making a total of 5 minutes in your whole life that you've spent thousands of pounds and years of your life for, that won't even necessarily significantly raise your chances of victory (factors like surprise, weapons used, multiple attackers, etc., make a huge difference).
Having said that, I've moved to Japan to study martial arts. Martial arts have a lot to give people, but I think self-defence is one of the most overrated aspects. In a lot of places in the world now, it's quite easy to avoid violence. For most of us, the chances of getting seriously injured in a fight are quite low. If you want to learn martial arts, do it for something that will make a difference in your life.