Like much of the world, in Britain a firm handshake, lasting a few seconds, is the common form of face-to-face greeting for all business situations and most social situations too.
Always use your right hand, and 'pump' the hand two or three times before you let it go. Ensure that your fingers grip the other person's palm, otherwise you will crush their fingers. Be careful not to clench in a bone-crushing grip, but do not offer a limp hand. Check that your palms are not sweaty or clammy before shaking hands.
Handshakes are brief, and should preferably be accompanied with direct eye contact. Do not complicate the greeting with other forms of touching - hands on the back, double-handed handshakes etc. Britain is still a comparatively non-tactile society.