Heat the blueberries, blackcurrants and one tablespoon of water in a pan for five minutes to release the juices. Set aside while you zest and juice the lemon.
Add the lemon zest and juice, butter and sugar to a heatproof bowl placed over a pan filled with gently simmering water and heat until the sugar has dissolved, then set aside for a minute or so.
Whisk the eggs well in a separate bowl, pour through a sieve into the bowl set over water. Add the fruit and the basil leaves. Keep stirring over a low heat for about 25-30 minutes.
Sieve again into a jug then pour into sterilised jars to serve.