Welcome to the Mudcat Jenny/NELLIE. Your mention of a school song book has stirred something in the old grey matter! I vaguely remember a singing game where everyone gathered in a circle while one person skipped around the circle singing something about a basket. This may just be a memory of A Tisket, A Tasket, but I seem to recall there were some exchanges which suggested courtship - but I don't think there were any primroses.

On the other hand, it is possible that somebody composed a song using elements from "Basket of Eggs", "Banks of Sweet Primroses" and perhaps "Claudy Banks" to make a song that was felt suitable for schoolchildren. Some of the folk songs that had been collected were bowdlerised so heavily for publication (especially for schools) that it is almost impossible to detect much trace of the original song. It came as quite a shock to me to discover that the old standard "The Oak and the Ash" comes from a very down-to-earth song!