Before you begin making the jam, place five saucers into the freezer which you’ll need to test the setting point later. Also prepare your jars and lids so they are properly sterile*.
Roughly chop the apples into small even pieces, without peeling or coring, then place in a large preserving pan with the blackberries. Heat gently until all the fruit has softened.
Remove from the heat, then pass the softened fruit through a sieve or food mill. You can discard the leftover seeds or keep for another purpose (like blackberry gin or vinegar).
Weigh the smooth fruit pulp – there should be between 600-650g. This is fine for the 500g sugar specified in the recipe. If the amount of fruit pulp varies wildly then adjust the amount of sugar accordingly.
Replace the seedless fruit pulp back into the preserving pan along with the lime juice and sugar. Heat gently, bringing up to a gentle simmer until all the sugar has dissolved.
Once the sugar has dissolved, turn the heat up and bring the jam to a rolling boil. Boil for 3-5 minutes then turn off the heat and test the jam to see if the correct setting point has been reached.
To test the jam’s setting point, drop a teaspoon of jam onto one of your frozen saucers. Wait 60 seconds. Push the jam with your fingertip, if it wrinkles up and leaves a clear trail behind your finger it is ready. If it is still too runny then turn the heat back on your jam and continue to heat at a rolling boil for a further 2 minutes. Keep testing the jam every 2-3 minutes until you are happy with the set of your jam.
Once the jam is ready spoon off the scum from the surface of the jam and then stir in the lime zest.
Decant the jam into the sterilised jars, screw the lids on tightly, allow to cool then label and store in a cool dark place.