Apparently there will be a new, June, published national Footpath map and if the ones you use are not listed then they cease to be so acknowledged. Apparently it takes 20 years for a footpath to become established. The only sources I've found for the means by which the public can make submission or inquiries are as follows:
Open Spaces https://www.oss.org.uk/need-to-know-more/ & email@example.com
Ramblers Association https://www.ramblers.org.uk/advice/improve-the-path-network/how-to-claim-an-unrecorded-right-of-way.aspx
Hampshire Rights of Way online provides an interactive map to identify paths. Please make your own further inquiries and let us know via our Contact Form if there is a better contact method.