A few example methods I have used:
Find a scene and composition you want. Get the camera in position, but take your eye away from viewfinder. Pre focus in manual focus, then wait. When a likely subject walks into the frame, take the shot.
or
Wide angle lens, shoot from hip on P or A mode, and capture the context, and trust your knowledge of camera and composition from experience. Be prepared to crop and adjust exposure in processing as required. With experience, your judgement will get more accurate.
or
Get close, in their face, and just take the photos. A lot of people will look weird at you, but won't complain. Some will moan and give you grief but you just smile and walk away. If someone really confronts you, delete the photo then make your swift exit. The key with this is to look and act normal. If you skulk, you will come across as dodgy. If you do it confidently, most people will not get suspicious of you. In UK law, there is still no privacy on public land, so you have every legal right to take photos of people. I cannot guarantee the public reaction, though.
or
Shoot with a telephoto, and from far away. Not as exciting results, but you'll get less hassle, and you have great control over composition and exposure.
Take your pick

However you go about it, I believe it's easier to seek forgiveness after the event. rather than to ask for permission in street photography.