Put the sugar in a large saucepan with 300ml water. Bring to a simmer then add the lemon zest and juice followed by the blackcurrants. Cook the mixture over a medium heat until the blackcurrants start to soften and burst.
Pour the mixture through a sieve lined with muslin into a clean, heatproof jug then transfer to sterilised bottles. Keeps in the fridge for up to 1 month.
Serve approx. 25ml of cordial per 100ml sparkling or still water, or dilute to taste.