The only tree I know that has smooth grey bark (when young anyway) is Ash, so maybe its a Fraxinus variety, possibly F. oxycarpa, although the leaves on that are thinner. Impossible to tell from the pic whether the leaves are toothed or not, looks like they're not.

I'm pretty sure you're right, and this is a walnut. My Mum had one in a previous garden and it looked just like this, with those leaves and the grey bark. I doubt whether you'll get any fruit, though, unless you're in the south. When we lived ina village in Buckinghamshire, we used to pick the fallen ones from an avenue of them, and they were delicious! Hopefully, you live in the south, but w're in Cumbria, and Mum only used to get small ones forming, which would quickly fall off. Best of luck, Annie