Hi Janet,
I can't give you the specific answer you're looking for on this one but perhaps I can clarify one or two things for you.
Firstly the original song 'Nice Cup of Tea' was written by the English humourist and playwright AP Herbert for his musical revue 'Home & Beauty' which was first performed in 1937 to celebrate the coronation of King George VI.
In the 1970s the song was used by Brooke Bond for their 'D' brand of tea so the lyrics became 'I like a nice cup of D in the morning'. I believe that the former F1 world champion Jackie Stewart and his wife Helen featured in the advert.
So the fact that 'tea' was altered to 'D' obviously meant that the jingle was recorded specifically for the ad rather than an old version of the song being used. Chances are that it was recorded by a session/jingles singer rather than an established artist which would make them almost impossible to track down 30+ years on.