After revisiting all solutions, a summary with some explanations:
android:autoLink="web"
will find an URL and create a link even if android:linksClickable is not set, links are by default clickable. You don't have to keep the URL alone, even in the middle of a text it will be detected and clickable.
<TextView
android:text="My web site: www.stackoverflow.com"
android:id="@+id/TextView1"
android:layout_height="wrap_content"
android:layout_width="wrap_content"
android:autoLink="web">
</TextView>
To set a link via the code, same principle, no need for pattern or android:autoLink in layout, the link is found automatically using Linkify:
final TextView myClickableUrl = (TextView) findViewById(R.id.myClickableUrlTextView);
myClickableUrl.setText("Click my web site: www.stackoverflow.com");
Linkify.addLinks(myClickableUrl, Linkify.WEB_URLS);
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