Look for a pot of gold...I'm fed up of seeing rainbows at the moment (much as I love them) because they're always precisely over the route that I'm cycling to and from work!
This post was a few years ago, but it wasn't a rainbow - rainbows are always opposite the sun. This sounds more like a parhelion of some sort - probably a sundog. They sometimes look like vertical rainbows, as here.There was a short vertical rainbow visible about 8:30 GMT from Loughborough, UK. It was due south and was coincident with what I thought at the time was the sun, but that has since appeared to the left. I checked a website that said the moon is below the horizon so I'm assuming it was a highly reflective cloud.