Yes, break of journey is permitted on either leg of all tickets between Honiton and Cowes East Red Funnel Ship. Via Eastleigh is a permitted route and thus you may break your journey there. Travel via Basingstoke isn't a permitted route.
If you got a ticket from St James Park (Exeter), for example, then travel would be permitted via Basingstoke on route "Honiton Salisbury" or "Reading not Lond" tickets. The former route of tickets are all approximately £10 more expensive than the equivalent tickets from Honiton, so that would appear to be a worthwhile price to pay given what Salisbury to Basingstoke costs.