Woman A Man Walked By is probably the most out-there song on the album: a Beefheart-esque snarl about a comic grotesque – a “mummy’s boy” with “chicken liver balls”  - delivered with an almost pantomimic relish. “That song is just enormous fun for me,” says Polly. “It’s very funny, and it’s great to perform.”

Which brings us to qualities much overlooked in some of Polly’s lyrics: mischief, playfulness, and the sense that contrary to the more crass understanding of what songwriters do, their work need not be a matter of aching earnestness. “I’ve got very used to being perplexed by this from an early age,” she says. “I have such enormous fun writing and singing music, and people very often take things extremely seriously, all the time. I find it really strange, as well, when I’m very obviously doing very silly voices [laughs]. There’s a part of Pig Will Not when I sound like I’m doing a Dalek impression.”

On the musical side, A Woman A Man Walked By features additional musical contributions from Polly’s close associate Eric Drew Feldman, the California-based drummer Carla Azar (from the left-field band Autolux), and the Italian guitarist Giovanni Ferrario. Quite apart from the cracked time signatures and shifting arrangements that occasionally give its songs the air of creations pulled from its creators’ irrational, emotional, sometimes almost dreamlike thoughts, it’s also streaked with touches that push it even further beyond the orthodox: on The Soldier, a ringing ukulele mends with the merest frosting of piano to absolutely haunting effect; 16.15.14 features a banjo part that lends it the flavour of sepia-tinted Appalachian folk music; elsewhere, there are parts played on wonderfully arcane and obsolescent keyboards.

That said, at the start of the album there is the aforementioned Black Hearted Love, the album’s lead-off single - a gloriously straight-ahead rock song that seems to have taken both of them by surprise. “Like all the things that become your favourites,” says John, “it happened quite easily and quite accidentally. There was no effort in writing a simple, straight-ahead rock song; it happened by itself. I can be very moved by something that is a really quite simple, quite straight-ahead piece music. I know that’s not what I’m known for, but those are often my favourite pieces.”

“I love that so song so much: it just feels like a great pop song to me, and there’s nothing I don’t like about it,” says Polly. “But it was like a freak child, really, because the others didn’t come out like that at all. I love that monstrous guitar riff that keeps on happening: it’s almost Morricone-esque.”

And so to the immediate future. Polly Jean Harvey and John Parish will soon be performing songs from A Woman A Man Walked By and Dance Hall At Louse Point on the live stage. When it comes to their respective solo work, John has “half an album” written, and Polly has already begun work on her next project, which she anticipates being co-produced by John, Flood and Mick Harvey. As to when the two of them might co-write another record, Polly claims the long gap that separated Dance Hall At Louse Point and this album points up the right way to go.

“I think it’ll be absolutely necessary to wait at least another twelve years,” she says.  “I’m serious: just think how great it’ll be. I was listening to both records over the last couple of days, and I loved hearing that journey. So I’m really excited to see what we can do another twelve years’ time.”

2021 is approximately 4350 days away. But don’t worry: on the evidence of A Woman A Man Walked By, the wait will be worth it.