James Derrick
Hi Steve, 

The way is tagged as highway=service, so I'd expect most 3rd party routing engines should include it in cycle routing:
http://www.openstreetmap.org/way/233642689

Some 3rd party routers take account of other keys, such as surface, smoothness or width, so it may help to survey and add these (and wait for the 3rd parties to download new OSM data):
https://wiki.openstreetmap.org/wiki/Key:surface 

There's no need to add lots of tags, as many are inferred (e.g. car=yes on a highway=service).

Keelmans Way does have surface tags, but is an explicit highway=cycleway anyway. If a highway is good for cycling, cycle=yes _might_ help as an extra hint.

Unfortunately, Google Maps and Streetview use copyrighted data which can not be used to add detail to OSM - and you may well know the actual 'ground-truth' way better than they do!
https://wiki.openstreetmap.org/wiki/FAQ#Why_don.27t_you_just_use_Google_Maps.2Fwhoever_for_your_data.3F

It's also worth checking the routing preferences - I sometimes forget to reset my Garmin to car routing after using it on the bike, causing much confusion.

You can check tags yourself by zooming in, using the Map Layers side bar, and turning on Map Data. 
If you get a feel for the tags on example ways, share your knowledge by editing the map, and close the Comment!