A few years ago we had a new cloakroom made. The guys who put the sink in, did not drill the hole properly, so the bottom of the hole is slightly larger than the base screws that hole it. The idea to use a small steel sheet to cover the hole and provide support to the wobbling tap.
I havent speced it yet. I am guessing max 10x10cm flat sq/rectangle piece, thickness somewhere between 2-5mm and the hole diameter will around 2cm. I can spec it up and take some pics when i get back from work tonight. As it wont be visible, any scrap metal should be fine as long as it can take he load of people using it every day.