This was one of the 'Watch With Mother' offerings in the 60's (along with Bill and Ben the flower pot men) - on Wednesdays I think. There was a woman reading stories from a big book with a string puppet dachshund to help her (he was called Sausage!).
There was always a story about a girl called Busy Lizzie who had a magic flower on her dress - when she touched it I think her wishes came true. There was also always a story about a group of sailors called the Jolly Jack Tars. I can't remember any more. Can anyone else?