Could it be a jasmine of some sort?

Definitely Jasmine, looks most like Jasmine officinale from the leaves, but if it is, in the ground it gets 35 feet by about 12feet or more, white scented flowers in summer.

Yes I have a Jasmine on our rose arch which looks very similar, beautiful scent.

I would also go with Jasmine. White flowers (summer jasmine), yellow flowers (winter jasmine).
I do like your comment that it is not a weed as it comes fom a GC, Lynda, they can sell some seriously weedy and invasive plants.

Thank you Every one. For Your Good Advice.On My Green Leaf Plant.I Did Giggle. When I Read One Of The Messages it Was From Bulbaholic. That Some Garden Cen Can Sell Seriously Weedy And invasive plants. It Just My Luck that's What It Is. A weed. Any way I'm Hoping it's Not a weed. And That it is a jasmine. And seeing that Summer Is Creeping Away From us,I Will Look Forward To Yellow Flower's. Thanks Again To you all.

Erm, you won't get yellow flowers. this is not Jasmine nudiflorum - it is a Jasmine for sure, and will have white, fragrant flowers, but you won't get flowers while its contained in a pot - it can't get big enough.

Hi Bamboo /Budaholic Says White For Summer.Yellow For Winter. I Will Have To Re Plant. But Before I Do I'm Going To Take A Bit To G.C to Ask What it Is .

Yea, but I can tell you that its 100% NOT the yellow flowered winter version, Jasmine nudiflorum, that Bulba mentioned. It might, though, be Jasmine humile - do any of the stems twine round themselves, or try to grasp nearby plants? if they do, its the climber, Jasmine officinale - if they don't, it might be Jasmine humile, which is a large shrub, non fragrant yellow flowers in summer.

Couldn't remember the specific names off the top of my head :-(