Looking at your activity, it appears that you did a U-turn right at the start of your ride, which would have then taken you off of the ‘London Loop’ route. In order to get the badge you have to select it from the start screen, and then not make any manual turns for the entire route. One you complete the route, and see the ‘route complete’ notification on your screen, you are free to make whatever manual turns you would like.
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