Do some excavation to see what is actually under the top layer--you may find several layers of flooring such as vinyl, linoleum, plywood or even hardwood if you are lucky. Once you get to the last layer, you may find your floors level.

It is odd that the only subfloor is in that room--mine don't have any at all, just the very thick tongue-and groove flooring itself laid directly on the joists. I need to do my own excavating in the kitchen--I know there are vinyl tiles (mine), 70s sheet vinyl (there when I moved in) and under that, who knows? From the basement I can see the same t and g boards as in the rest of the downstairs, so I'm hoping it is oak to match the rest of the first floor. My ideal find would be original linoleum in a nice pattern I could use!

Whether you could install new flooring as you suggest depends on your joist spacing, the thickness of the flooring, and the weight of your cabinets and appliances. When I moved in, my kitchen had a stove in front of the chimney breast, a refrigerator blocking the only window, and 70s plywoodish cabinets along that wall and forming an ell on the neighboring wall. There was no sag or deflection of the floor. My kitchen is about 12x12, so the span isn't too great, and there is bridging between my joists as in most 1900s houses.

I redid my cabinets to cover the wall to the right of the window (found the original doors in the garage and built my own boxes), moved the fridge to the pantry, and replaced the stove with a newer one of the same size in the same spot. Yes, I should have done the floor research at that time, but I just wanted the 70s crap gone. :) That sheet vinyl was under the cabinets, so it was put in before they put the cheap ones in--but it wasn't close to original to the house.

If you opt for huge fridges and restaurant size stoves, you may have a problem--but my appliances are standard sizes since I'm just an average person and not a professional chef wannabe. Food tastes just as good done on normal appliances--it is all in the ingredients, not the utensils.

It's very very difficult (and EXPENSIVE) to find old wood in long enough lengths to span the entire room's width, which is what you'd need to do if you eliminated the subfloor. You'd also have a LOT more flex than with modern floor systems. The opposite direction would be a better choice. In other words, remove the old flooring, install a subfloor (with proper insulation under it) and then relay the old wood. You'd have less flex, warmer floors, and the same height throughout the home.