Bring 1 cup of water to boil. In a heatproof cup or bowl, pour the boiling water over the ginger slices. Allow to steep for 20 minutes, or overnight. Stir in the raw honey.
Remove the leaves from the bottom of half of the tarragon sprigs and add to the ginger water, followed by the Pimms, and lime slices. Chill for 10 minutes, then add the soda water.
Fill 4 punch, Tom Collins, or pint glasses with ice and divide the Pimm’s mixture between them. Garnish with two cucumber wedges and the remaining tarragon sprigs.