Were the blooms red? What I see there is plants that die back to the ground each year, which explains all the dead wood. Each year, they start over again with new canes. I suspect this was originally a grafted rose and now you have root stock growing. The rootstock is most likely Dr. Huey, which is a once bloomer that resembles some old red roses. The originally purchased rose is long dead. That's my guess. If you dig down a bit and see a big knot, that's the graft. If there's no knot, you have an own-root rose, and it could be an antique, or what you are calling Old English. But if it was planted 20 years ago, that's not likely, unless it was moved there from another garden. So many possibilities!
If you decide to dig it out and move it to a sunnier location with no tree roots nearby, I'll warn you that digging it is a horrible chore. The roots will be deep and huge. We're talking back breaking, all-day chore to dig and replant a rose that might not survive the move.
What I would do is, as others said, cut out all the dead wood first. A cane that shows some green is a live cane, and I do see a few of them in your photos. Cut a few inches off the live canes also to stimulate a bit of growth. Do this when the forsythias in your area start to bloom. I would buy a few bags of compost and spread them around the roses, and water it well. In April, I would start fertilizing. Give it fish emulsion, miracle grow, alfalfa pellets, milorganite, superthrive. Keep watering regularly. With this treatment, any rose should be blooming by June.
Once they bloom, post a photo of the blossoms and leaves, and everyone can take a shot at guessing the name and type of rose. It would be wonderful if it turns out to be an OGR....Old Garden Rose, or antique. Good luck!
