yeh bizaare, must there must have been ammonia
somewhere, because you are getting high nitrite readings, so the filter media is processing the ammonia, hence the ammonia is going down.
it usually takes longer for the nitrite consuming bacteria to develop, hence when cycling a tank, ammonia usually rises and drops quite quickly (matter of a few days in my experience) and then nitrite rises, but then can take anything up to 21 days in my experience for the nitrite to come down to 0.
i think one thing to consider now Alice

is to ensure there is some continuing ammonia source for your filter media. Just a little bit, have you got any fish food lying about, as you dont have to get pure ammonia.
i would not advise adding too much ammonia (as in food) as your tank is already half-way or thereabouts through the cycling process. If you add too much ammonia now it would make your cycling process uneccessarily long.
basically, once your ammonia level in tank gets to zero on a test kit during the cycling you then need to continue to provide the filter with a "food source" i.e. ammonia, this could be done by
(a) using fish food, pure ammonia or something like prawns
(b) adding fish (just one or two) fish excrete ammonia through their gills and poop!
I would suggest only adding fish once Nitrite hits 0, this will mean your fish go into the tank with good water quality already in place.
Once your ammonia and nitrite are at 0 you are good to go! I would advise stocking slowly to check just how "bedded in" the filter bacteria are.
The key is the
continuos ammonia source, or you start to lose bacteria from the filter and risk going back to square 1
