I'd advise everyone to take a bottle of formula with them in their hospital bag.
I experienced exactly what they were talking about on Woman's Hour. My baby still hadn't breastfed by day 4 (despite persistent trying, using breastpump to express, everything) and the midwives did nothing about it.
Every single one (and there were about 8 because they are all agency and you get a different one each shift so nobody takes overall responsibility for you) just ticked on the sheet 'mother breastfeeding' and that was that. When I tried to explain that he wasn't getting anything they just weren't interested.
I was so worried because I know that adults can only live about 5 days without water. It never entered my head that I should give him formula until the woman in the bed opposite me suggested it. I have no idea why I didn't think of it, I'm not particularly anti-formula, but I think it's just drilled into you that you have to breastfeed.
I sent my husband down to the midwife's desk to get some formula and they were really funny about giving it to him - presumably because they have breastfeeding targets (though you'd think they'd pay more attention to their baby survival rate targets).
When I gave him the formula, you could literally see his whole body relax. He'd been screaming constantly for 2 days before. Anyway, he still ended up with jaundice for about a week because he hadn't had enough liquid to get rid of the toxins in his blood, which wasn't nice but better than him being dead, which I honestly think was about 24hrs away.
When I got home, I did manage to resume breastfeeding. I fed him combined breast and bottle til he was 6 months old.