I feel very conflicted on this. I'll declare an interest; when my children were young I trained as an NCT Breastfeeding Counsellor, so I'm clearly very pro.
I am shocked at the statement that the UK has the lowest breastfeeding rate in the world. There should be no physiological reason for this. Yes, there are people who are unable to breastfeed but, even allowing for the fact that in the past the genetic inability to breastfeed would have meant that girl children who inherited that inability would be less likely to thrive (or even survive) and have children of their own, while, now, with decades of bottlefeeding behind us, together with improvements in formula, they do survive to pass the inability on to their children, I cannot believe that the UK has more mothers than anywhere else in the world who are unable to breastfeed. So there must be cultural reasons for such a low rate.
Of course, culture is very difficult to change; it might just be that a financial incentive has sufficient clout to change some minds. I'd be interested to know if this proposed initiative is based on any studies which show that it increases breastfeeding rates.
But I think another aspect is the quality of support that a mother gets if she's having difficulties. I know that it is being well promoted from the medical side (midwives, health visitors) but peer pressure and family are very influential. If you are struggling in the first few weeks with your first baby (and I know, from experience, how much determination is needed to persist)and you are surrounded by family and friends who have all bottle fed it is far more likely that you will give up with their approval; and it is their approval that counts far more than does the approval of midwives and health visitors. This was a problem 30+ years ago when I was counselling and it doesn't appear to have got any easier.
So, if studies show that a financial incentive has a positive effect then I think it is worth a try, regardless of the expense. There are worse things that the money could be spent on.