The deep red flowers are from the rootstock. It is more vigorous than the variety grafted onto it and will eventually take over if not cut back to the crown of the plant.

That was my first thought - but it doesn't seem to start from below the graft line and it doesn't have the usual sucker appearance: thorny, very fast growing, 7 leaflets etc.
Elizabeth

The description sounds like Dr. Huey - a rose that is used a lot for root stock. I had a similar experience with Austin's "Tamora" and was told to grab the cane as close to its origin as possible - a pliers helps - and yank the cane off.

BettyN

It really does sound like Dr. Huey. You said that this is above the graft line, but are you sure? Can you show us a picture of the cane above the graft line? It is just the obvious answer, so without more details it seems like the most logical answer too.

I think you are right - it is close to the graft line but may be below, so I've removed it. Thanks again. (Now that it's been pointed out I think I have spotted several more Dr Hueys in other places such as school yards etc.)

Mary Rose sports quite easily. I've had blooms in every shade of pink (the lighter ones have been cloned and named by Austin) some half dark/ half light pink, others speckled and striped and of course the form changes too, barely double, button center, very double, etc. It's a great rose and when in full bloom you can smell the fragrance from several feet away.
It sports in pink however, not red. Dr. Huey is a beautiful rose but is a once-bloomer (although I have read about an everblooming strain).

My Mary rose sported white. I'm told that one of its parents is Winchester which is white. It only did it once, a couple of years ago, and my neighbor's Mary rose sported white at the same time. And never again. Hmm.