The best way to turn off journey notifications at the moment is to disable push notifications from the By Miles app on your phone.
To do this on an iPhone:
Open your Settings app
Tap Notification Center on the left-hand side of your screen
Swipe up until you see a list of your apps
Find By Miles, tap it and choose None for notification type
To do this on an Android phone:
Open up Settings
Go to Apps or Application Manager
Click By Miles
Click App Notifications and disable the 'ON' toggle