Riding Down to Portsmouth is number 1534 in the Roud Folk Song Index. It hasn't been found particularly often in tradition; Sharp, Vaughan Williams and Grainger noted versions, and sets have been recorded from Tom Willett (by Bill Leader and Paul Carter in 1962) and from Mary Ann Haynes (by Mike Yates in the 1970s). That's about it. I don't remember anything about June Tabor's recording, but it will be an arrangement of one of those. June's singing is rather mannered, and it can be hard to understand sometimes. Does she credit her source in the sleeve notes?

There are two broadside editions at  Bodleian Library Broadside Ballads. The final verse won't be very different, I'd think, from whatever she sang.

Riding down to Portsmouth