Karen Bassey starts out sounding like a greeting card. Love is a rainbow: beautiful, colourful, and without a beginning or an end. Those are the things we expect to hear, and the short, simple lines make it feel safe and familiar.
Then the speaker turns to "our love", and the comparison curdles. It is still beautiful, but only "to the mere man", which suggests that outsiders see something lovely while the people inside the relationship know better. The repeated phrase "no beginning or an end" now means something much bleaker. Earlier it meant love lasting forever. In the last line it means the love never really existed: "it is non existent."
The mood shifts from admiring to disillusioned, with a quiet, bitter sting at the end. A rainbow, after all, is something you can see but never touch. The speaker seems to be saying that their love was the same: a pretty appearance with nothing solid behind it.