The construction of Hinkley Point B, which was undertaken by a consortium known as The Nuclear Power Group ('TNPG'), started in 1967. The reactors were supplied by TNPG and the turbines by GEC. Hinkley Point B is an Advanced Gas-cooled Reactor (AGR) which was designed to generate 1250 MW of electricity (MWe).

In March 1971 it was announced that there would be a six month delay in completion due to problems with the insulation of the concrete pressure vessel. In place of the stainless steel mesh and foil insulation that had been used on previous Magnox stations, a fibrous type of insulation supplied by Delaney Gallay, part of the Lindustries Group, had been used for the first time. During pre-operational trials, before the nuclear fuel was loaded, high levels of acoustic vibration in the gas circuit were found to be damaging the insulation tiles, and the retention plates which held the insulation in place had to be redesigned and modified within the reactor.

During further pre-operational testing, severe vibration of the fuel channel gags was detected. The fuel channel gags are valves which are gradually closed to restrict the flow of gas through a fuel channel in order to maintain the channel gas outlet temperature as the nuclear fuel is used up. Modifications to produce a fluidically generated bias force to stop the gags vibrating took time to design, test and implement, delaying the planned start up date. The station began generating electricity on 5 February 1976.

It was taken over by Nuclear Electric as part of the privatisation of the UK Electricity Supply Industry in 1989, though remaining in public ownership at that time. In 1996, the AGR and PWR assets of Nuclear Electric and Scottish Nuclear were privatised as part of British Energy.

In 2006 the station's reactors were closed for testing microscopic defects that had been found in similar reactors. The media implied that defects were gaping holes gushing steam. Had this been the case, the plant would automatically shut down at the slight loss of pressure. Due to the fact it is ageing, it will, if it returns to full service, only generate 570 MW per reactor instead of the rated 625 MWe, in total producing 1140 MWe. However on 16 August 2006 the company warned that until a decision was made over whether to extend its usable life, it would operate at a maximum of 70 per cent load. Both reactors were subsequently restarted generating 420 MWe each, roughly 70% of full power. The number 4 reactor was cleared for restart by the Nuclear Installations Inspectorate on 11 May 2007. The power station current accounting closure date in 2016, though it could possibly be life-extended beyond that date.

Hinkley Point B is one of four nuclear power stations in the area, the others being the adjacent Hinkley Point A together with Oldbury and Berkeley (being decommissioned) on the banks of the River Severn. A new Hinkley Point C nuclear power station is under consideration.