The term V-Bomber (or just V Bomber) refers to the aircraft that were built by Great Britain as a strategic nuclear force in the 1950s and 1960s. The name comes from the fact that their model names all began with V. Although a firm ally of the United States, Great Britain always insisted on retaining an independent nuclear deterrent to avoid being dependent on the U.S. This desire was focused and sharpened by the Suez Crisis of 1956, when the U.K found itself on the opposite side from the United States during the English, French and Israeli invasion of Egypt. Following this, the British were determined to prove that their nuclear strategy and related foreign policy was not dependent on U.S. approval.
The first V-Bomber, the Vickers Valiant, was already active during the Suez Crisis. First flying in 1951 and beginning deliveries in 1954, the Valiant was in service with the RAF when the invasion occurred. The Valiant was the epitome of the Doolittle/Douhet school of 'the bomber will always get through' - it was high-flying and fast, designed to deal primarily with cannon-armed interceptor aircraft. Air-to-air missiles immediately made it a vulnerable giant, and it was produced mostly because it would be available quickly and lessons could be learned. As a result, the Valiant had been mostly decommissioned as early as 1964, with a few holding on as photo reconnaissance aircraft.
The second V-Bomber (and the most famous, and the only one to have dropped weapons in anger as far as I am aware) is the Avro Vulcan. Nicknamed the 'Tin Triangle' for its enormous delta wing, it first flew in 1952 and came into service in 1956. The most successful, this bomber was operated until 1984, with a series of conventional weapon bombing missions on Port Stanley during the Falklands War its only combat experience.
Finally, the Handley Page Victor also flew for the first time in 1952 and was accepted in 1956. Crescent-winged for better high-speed cruise performance, it was an extremely expensive aircraft to procure. As a result, the decision was made to consolidate the bomber force on the Vulcan, and most Victors were withdrawn from service in the 1960s. Several, like the Valiant, survived as high-speed recce platforms, as it was at the time the largest supersonic aircraft in the world.
The V-Bombers were phased out due to the immense cost of maintaining them. By the 1970s, Great Britain had acquired and centered its nuclear deterrent on its own set of SSBNs - originally Polaris, later Trident - and there was no appetite for maintaining two separate deterrent forces. As the bombers were more vulnerable, they took a back seat, and the funds freed up were put into fighter-bomber and other tactical aircraft programs.