Finding DISTANCES on longer bike/hike paths I want to bike along the Oxford Canal for several days.  I need a way to determine distances to plan for where to sleep and eat.

Mapping apps tend to tell you where to go instead of telling you about where you decide to go.  

Are there any websites or apps¹ that make it easy to determine the distance along a path I will indicate?

¹I prefer IOS, but I do have an Android device.
I use Google maps (set to 'cycling mode') and Strava to plan routes. Both try to find the 'best' route between the start and end points but allow fine control of the route by setting intermediate waypoints.

Each will give you details of the route including distance and a gradient profile.

Google maps tends to find routes based on cyclepaths, bike friendly roads and trails. Strava uses its 'heat map' built up from recorded rides. Both have their pros and cons.  It can be a bit of a struggle to get both Google maps and Strava to adhere to a specific route, but it is doable with judicious placement of waypoints. Strava can be made a little more controllable by turning the 'use popularity' option off.

I tend to use Strava if I want to upload the route to my Wahoo bike computer app.

I've not used RideWithGPS but I assume it has the same fine control over route planning.