Yes you can.... and it will probably fare up better than my electric stove with yorus being cast iron. Canners get heavy and destroy stove elements.
The good news. Is on your burner plate to boil, you can use it for canning. I have friends who can on woodstoves as they are off grid and have nothing else, so they can be tricky to regulate for heat too. Your Aga might not be easy, it might be easier, it might take awhile to get to the right temp. But it is more than likely possible for you.
For a water bath canner, just keep it at a boil. So as long as you can get it hot enough to bring to a boil and stay there, that will work for waterbath canning. When you bring it to a boil, you should be able to play with the heat dial (or whatever it has on your stove) and not have it on full blast the whole time.
The same should be ok for a pressure canner. You put 2-3" of water in the bottom and bring it to a boil with the top lid on, let it vent out of the steam vent for 10 minutes, and then seal it up with your weighed gauge or dial. Then you keep it at that temperature for the right pressure and time according to your recipe and elevation. Like on my electric stove, I can turn it down to 6 on the dial (out of 9) and it will stay at pressure. So you will likely not have to crank it up on high the whole time you are processing. The trick is to find where the happy spot is on your regulator. I think I would do something like jam or juice for a test run or two. Something you can reprocess or not cry about if it fails (such as meat).
Good luck to you,