Empson
I've had a look in the trade directories for the 50's and 60's and can find no mention of a florist all, nor any type of a shop owned or managed by anybody called Reeves. Though this doesn't mean that there wasn't such a shop as it might have been listed at a fruit shop or a greengrocers previously and was never changed.
My grandparents lived in Vincent Street until it was demolished and I lived there myself in the 50's and I don't remember anyone by the name of Reeves, but it was a big street and the whole middle section of it was bombed out in the 40's.