My parents never let any of their 3 cockers upstairs - the only time they went up was being carried for a bath (so maybe they didn't want to go upstairs anyway as that was their association with it!). The last one used to sit at the bottom of the stairs waiting for my mum. A stair gate would make it easier to stop him, but just removing him and saying "no" should be enough. I'd stick with the rule - much easier for the kids' toys (which could be fatal if the dog swallowed something sharp).
We live in a flat which has two stairs - one "up" to the bedroom and one "down" to the living room. We're trying to train Henry to realise that the bedroom is out of bounds - removing any time he ventures "up" there, but he is allowed in the hallway, as this is the way to go out! It's quite tricky, but he seems to be getting the hang of it (now he's big enough to actually jump up the stairs!).