Wash your bramble berries, picking out any foliage or twigs. Leave to drain in a sieve or colander while you prep your jars.
Preheat the oven to 200°C/400°F. Clean 5 450g glass jars and lids, scrubbing them in hot soapy water and rinsing well. Place the wet jars in the oven to dry out. Turn off the oven after ten minutes and leave the jars in there until you're ready to use them - keeping the jars hot ensures the glass won't crack when you pour the hot jam into them.
Put a few small plates into the freezer. You'll use these for testing the setting point of the jam.
Add the chopped apples and the water to a large pan and warm over medium heat for a few minutes. Add the bramble berries and cinnamon. Cook for five minutes, or until the bramble berries have released their juices.
Add the sugar and the lemon juice to the pan and stir well until the sugar has completely dissolved (about five minutes). Bring the mixture to a boil, and maintain a rolling boil (approx 104°C) for 15 minutes.
Take one of your small plates out of the freezer and spoon a teaspoon of hot jam on to it. Allow it to cool, then run a finger through the centre of your jam puddle. If the jam is set, it will hold its shape and the channel you made with your finger will remain clear. If the channel floods, your jam is too runny. Return it to the heat for a few minutes before testing it again.
Once your jam has reached setting point, turn off the heat and add the half teaspoon of butter to the pan. Stir until dissolved. The butter causes any scum or foam that formed on the surface of the jam to dissipate.
Take your jars out of the oven and place on a heat proof mat. Carefully fill the jars with the jam mix. I find it easiest to first tip the hot jam into a large measuring jug, and fill the jars from that. Screw the lids on tightly.
Your jam should last for about eight weeks once opened, or two years unopened.