If you cannot get to Terry White Chemmart, there are other options.
All-foil blister packs:
All-foil blister packs made of aluminium foil can be recycled directly into your own yellow recycling bin, as long as they are larger than a credit card.
If smaller, they fall between the grates of the recycling equipment and end up in landfill.
Small individual packs can, however, be crushed into a golf ball size object and recyled in your yellow bin, as with other foil.
Foil-and-plastic blister packs:
These can be identified simply by looking through the space where the tablet was; if transparent or white, they are the combined foil and plastic. These are more difficult to recycle, needing a different process.
Terracycle offers a box where blister packs can be collected to be recycled, but it comes at a cost and will only be available in specific locations.
So, try to get to Terry White Chemmart!