In a cocktail shaker, add 2 basil leaves and gently muddle. Add the simple syrup, ginger beer and pink grapefruit juice and a few ice cubes. Swirl to mix.
Fill a highball glass with ice and add the Pimm's No. 1. Strain the cocktail shaker contents into a glass. Garnish the drink with fresh basil leaf, cucumber and fresh ginger slices and serve.