Grease a 1.2-litre pudding dish with butter, add golden syrup, and scatter in blueberries.
Whisk the remaining pudding ingredients together until fluffy and spoon into the dish.
Cover with baking parchment and foil, tying securely with string to create a handle.
Place a tea towel and upside-down saucer in a large saucepan and half-fill with water.
Place the pudding on the saucer, cover the pan, and simmer for 1.5 to 2 hours.
Bring milk, cream, and vanilla to a gentle boil in a saucepan.
Whisk sugar and egg yolks together in a bowl until pale.
Pour the hot milk mixture over the eggs while whisking continuously.
Cook the mixture over low heat until thickened enough to coat a spoon.
Strain the custard into a clean pan and keep warm.
Turn the pudding onto a plate and serve with the warm custard.