Yes, safety should not be a problem. London is one of the safest large cities in the world, and there are few if any areas that one should not venture at any ordinary time (including after dark). As always, anywhere, one should stay alert and be aware of what is going on around one. In highly touristed areas (like the southern end of Edgware Road, near Oxford Street) we are warned about pick-pockets, and certainly one should be alert to the possibility that they are acting there. How common pick-pocketing and other petty crime like that really is, I do not know.