Paul,
Whilst we are not going to discover a Harry Cox any more, bits and pieces of interest are still turning up. In people's attics are old manuscripts with these songs in. I know I have recently been sent some.
Families still have old tapes lying around in a dusty box, of grandad singing his old songs.
Here's quite an exciting example. As a collector of songs in the 1960s it was always a pain to me that we never collected any songs of any note that referred to my home town of Hull. In the 80s I had a ceilidh band I ran and we needed desperately a new lead musician. A young accordionist who had nothing to do with folk was suggested and being keen and a music reader he quickly picked up the band repertoire. After being with us for about 10 years he remembered he had an old cassette tape of his previous accordion band in the loft. The recording was of the band playing at a senior citizens outing. They had left the tape running in an interval and an old lady just stood up and sang a version of the Gaol song specific to Hedon Road Gaol in Hull. Wonderful stuff! You can hear me singing it on the Yorkshire Garland website. There are many millions of people in the English-speaking world. Some of them must still have these old recordings that would be useful to us.
Apart from this, almost on a daily basis this very forum turns up interesting unrecorded pieces.