What are the benefits, if any, of using a pizza stone in a toaster oven?
In a small toaster oven, using a pizza stone is likely to be a tradeoff:


Toasting -- counter-productive, because it will shield the bottom of the bread (or other item) from the direct radiative heat from the bottom elements; you would want to remove the stone for this use.
Broiling (or as it is called in the British parlance if I understand correctly, grilling) -- Probably not a good idea.  In a full sized oven, the stone would be left far enough from the heating elements that it would not be subject to intense radiative heat.  In a toaster oven, it might be too close to the elements when the oven is used this way, so might be subject to cracking due to a higher temperature gradient and uneven thermal expansion.
General baking -- will require a longer a pre-heating period for the oven/stone to come up to temperature, but once at temperature, will provide a buffering effect for more even heating.  
Convenience -- in full sized ovens, people often leave the stone in all of the time, and cook on a different rack if they don't want direct contact with the stone.   This may or may not be possible or convenient in a toaster oven, so you may be constantly removing or putting back the stone based on your current use


Note that all of the above is just reasoning based on known facts; I haven't tried a pizza stone in a toaster oven, and wouldn't do so, as they have a generally low thermal mass.   I tend to think of them as tools for toasting and reheating, not for primary cooking, baking, or roasting.