In answer to your original question, I don't know. But, GPS in general is pretty awful at working out elevation. It really is not one of the system's strong points.
Originally Posted by JonPaulWild: “Is there any free software or add-ons for my Tom Tom One so that it shows me the elevation / altitude in the area I'm at?”
You may struggle to find anything that works with recent versions of the TomTom firmware.
TomTom killed off their Software Development Kit which was used to develop add on for their products some time ago. It looks like that means there is little if anything still around that will run on the current version of firmware.
which is not free but no idea if it works with the current version of TomTom firmware. Doesn't seem to have had much development in the last 6 months or so from the website.