Place the strawberries and blueberries in a large saucepan over medium-high heat.
Add the honey, lemon juice and lemon zest and boil, stirring every now and then, until the mixture thickens. With my really soft and juicy berries, this took about 35 minutes. It could take more or less time depending on your berries.
To test, put some of the jam on a clean spoon and then put the spoon on a plate in the freezer. Let it sit in there for five minutes and then take it out. If the jam doesn't fall easily off the spoon when you turn it to the side, it's ready and you can take the pot off the heat. If it does pour off easily, continue cooking for another 5 minutes and try the test again.
Let cool and then pour into jars and store in the fridge. Yields about a 600ml / 20oz jar. It could be more or less, depending on exactly how long you cook the jam. I kept mine in the fridge for 1 1/2 weeks before using it all up and had no problem with it going bad. Freeze if storing for longer than that.