When I provided a link to 'Off-Peak and Super Off-Peak ticket terms and conditions' on the National Rail website, above, I was surprised that there was no reference to 'break of journey', as I could have sworn that I'd seen it there before.
I've now discovered that there are TWO web pages on the matter, with this one being the more detailed:
http://www.nationalrail.co.uk/times_fares/ticket_types/46590.aspx
From reading that, a break of journey is always permitted on the return part of an Off-Peak ticket and usually (but not always) permitted on the outbound portion. So it seems that enquiring at Longfield might still be the best way forward!