In 2130, Earth has attained a clean, safe and anaesthetised future. Dominick is a time traveller whose job is to observe transport systems on the 'flipside' - the era before the Time Barrier was broken. Dominick's 'Circuit' is London 1980, where he believes he may have an ancestor - his great-great-grandfather, also named Dominick Hide. Breaking the rules, Dominick lands on the flipside to search for his great-great-grandfather. London of 1980 is a very different place to London of 2130, and Dominick is completely unprepared for the amazing culture shock of Portobello Road. He has no money, and almost no idea how to behave. He concocts a story about finding a 'distant relative', and to avoid suspicion, calls himself Gilbey, after a brand of Gin. While he is on the flipside, he relies entirely on the kindness of strangers, including the owner of a clothes shop, Jane Winters. After an unsuccessful visit to the flipside, Dominick returns to 2130 determined to try again. Dominick tells his wife, Ava, that he plans to visit the flipside. She is upset and confused, and asks him not to go. Despite the risks involved, and the promise of trouble from his superior, Caleb Line, Dominick visits the flipside again. While he is there, and against all sense, Dominick begins a relationship with Jane. Still Dominick has not found his great-great-grandfather, but now his visits seem to be more concerned with seeing Jane than with finding the elusive 1980 Dominick. They spend a weekend together at a guesthouse in Herne Bay where his flying saucer has been taken. As a result, Jane becomes pregnant. When Dominick learns this, he goes to Caleb Line to admit his guilt, whatever the consequences. Caleb reveals that he was aware, all the time, of what Dominick was doing. He sanctioned it because Dominick Hide is the victim of a "genetic time-slip" - he is, in fact, his own ancestor. The child Jane is carrying will be Dominick's great-grandfather. Caleb tells Dominick that further landings on the flipside will not be permitted, officially, implying that he trusts Dominick enough to turn a blind eye to further landings. However, having narrowly avoided causing a fatal accident on a previous landing, Dominick realises the danger involved, and decides to visit the flipside just once more, where he provides for Jane and his son by fetching them the following week's newspaper, from which Jane can use the soccer results to win the football pools. He explains that this will be the last time he can visit the flipside and says a sad farewell to his great-great-grandmother. Jane watches Dominick take off in his flying saucer, convinced at last that his story is true. The closing scenes show Jane recording her son Dominick at Herne Bay in 1988 and Dominick and Ava walking and laughing in the surf at the Herne Bay of 2130 with their own baby.
The play was successful enough for a sequel to be commissioned, and Another Flip For Dominick was broadcast in 1982. The original play was repeated the week before the sequel aired. Neither play was shown again on British television until 26 February 2006, when The Flipside of Dominick Hide was broadcast on BBC Four to tie in with a series of programmes about time. The two dramas were released as a double VHS video pack in 1991 and on region 2DVD in 2005.