When my toilet appears to be blocked it never is. The "blockage" is downstream in the inspection pit outside.
Before messing around in your WC pan check to see if there's an inspection cover (manhole) outside - lift it and look inside - if empty then you have a blocked toilet - if partially full the inspection pit has a blockage in the outlet pipe - the one pointing towards the street. When this happens to me I clear the blockage by trying to pull the obstruction back into the pit with a long pole.
If you do need to resort to the Brush and Bag solution a plastic bag is wrapped around the head of the brush in an attempt to make a rudimentary plunger.
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Peccavi
January 2011