The original ad (below) ran in the 1970s and 1980s. It was created by Allen Brady and Marsh, which was later taken over by Lowe.
The famous jingle was penned by Rod Allen, who passed away in 2007.
The new ad, created by PR agency Taylor Herring, again features actor Julian Chagrin creeping down the stairs in the middle of the night into the kitchen to get his R Whites fix.
This time, instead of opening the fridge to find R Whites lemonade, Chagrin opens the freezer to reveal the brand's lemonade lolly pops.
Chagrin is again joined by Harriet Philpin, who played his wife in the original, in the kitchen as the well-known soundtrack plays out.
The song was originally written by Ross MacManus, Elvis Costello's father. It has been re-recorded to include the lyrics, "I'm a secret lemonade licker".
The ad was created after the agency contacted Chagrin and conducted a national search for Philpin, who has been living in Ireland.
She was eventually notified of the search by her son, who had seen an appeal printed in the UK national press.
The ad launched last night on UKTV's Gold channel to mark the start of National Ice Cream Week. It will run in intermittent bursts.
Taylor Herring bought the media space directly from Channel 4, and used production company iCity Media.
Jenny Bostock, Britvic licensing partner, Frederick Dairies, said: "R Whites is a much loved and iconic British brand.
"We couldn't thinks of a more fitting way to mark its enduring appeal and the launch of the new lolly that to reunite the original cast."
The R Whites brand is owned by Britvic, however it has licensed its name for the ice lollies to Fredericks Dairies, which holds similar deals for Cadbury and the Robinson's Fruit Shoot brand, which is also owned by Britvic.