Thanks. Looking at the Bing aerial and street side imagery, the 5 mph limit and informal zebra crossings indicate that it's not a public highway. Despite this, it still appears to be officially called Ossory Road from its Designated Street Name USRN. I've updated it and tweaked a few other things nearby in https://www.openstreetmap.org/changeset/162781378

It may take a couple of weeks before cycle routing software "knows" about either of our edits, depending on how often they update.