Hang on there a minute. There's a much easier way to clear a blocked loo than putting your hand down it
or taking it apart.
I too had the situation where one of those toilet cleaner thingys that hang onto the lip of the bowl came loose and went down the pot only to get stuck. I went to B & Q where I bought a "drain bomb". This is essentially a large plunger similar to a bicycle pump on steroids. It comes with a large seal at one end that covers the mouth of the neck of the bowl.
What you do is put it down into the blocked loo. You then pull up the plunger which sucks some of the water up and then you push the plunger back down and the force of the concentrated water pushes the blockage through to the sewer. This worked first time for me and the toilet cleaner thing was pushed out to the sewer where I fished it out and binned it. This plunger also comes with a smaller attachment for clearing blocked sinks, showers etc.
I've seen these drain bombs in Woodies and Atlantic. It only cost me about €10, and it cleared the blockage in seconds and no smelly hand for me