Earthsearch
Three crew-generations previously, the starship Challenger - a vast ten-mile-long survey vessel – was launched from Earth on an interstellar mission to search the universe for an Earth-type planet to colonise. This has been unsuccessful, and the ship's once enormous crew-count has now been reduced to four. Telson (the ship's Commander), Sharna (Science officer), Darv and Astra are the third-generation crew- the only survivors of the disastrous Great Meteoroid Strike which seriously damaged the ship two decades previously, killing the entire second-generation crew and rendering large areas of the ship "uncontrolled" and inaccessible to its electronic systems.
From infancy, the four third-generation crew members (now in their early twenties) have been raised by robots and by the Angels – mysterious unseen beings who run the ship and who only manifest as disembodied voices. Darv, the most sceptical and enquiring of the crew members, suspects that the Angels are merely computers; but the others consider them as "Guardian Angels" and work entirely under their guidance.
With no suitably colonisable planet found after over a hundred years of searching, a crew-vote is taken and the Challenger sets a course for the return to Earth. Darv and Astra, while exploring one of the uncontrolled zones, find a survey recording of an Earth-type planet called Paradise. (In the accompanying novelisation, Darv is alone when he makes the discovery.) As is standard procedure, the crew enter suspended animation in order to prevent ageing and possible death during the many years of journey time.
Unrevealed to the crew, the Angels (who are the ship's control computers; their name being an acronym of ANcillary Guardian of Environment and Life ) have their own agenda. They desire absolute control and mastery over any colony resulting from the mission. To this end, they covertly engineered the apparent accident which killed the second-generation crew (who would otherwise have ended the mission before the Angels wanted it to end) and have kept the third-generation crew sexually immature and innocent via drugs and disinformation in order to keep them more tractable. However, their machinations have begun to backfire already. Their requirement of a minimum human crew of four to man the Challenger's control room requires the Angels to work mainly via suggestion and manipulation. Also, the Great Meteoroid Strike damaged the ship and their control over it more than was planned, including damage to their own memory banks, which in turn deprived them of vital information about the Theory of Relativity. Concerned that the discovery of the Paradise recording may convince the crew members to change their plans, the Angels suppress Darv's and Astra's memories of the survey recording by hypnotic manipulation, in Darv's case by using violent, nightmare-inducing imagery.
Found with a search for bbc serial "computer * angel"