Actually they are right. In fact it is only a proportion of the money we give them since the UK are net contributors (with our contribution set to rise considerably over the next few years (if we were to remain). By the same token you are IMO correct in that the EU is not concerned with domestic politics so they are not London/SE centric when it comes to development funding. So whilst ...'technically' their response to you is correct but your response is more accurate in reality. If BJ WAS a man of his word, and sticks to the script of his manifesto (....pause for hysterical laughter...) then more monmey would be available to develop the' Northern Powerhouse' infrastructure etc. However I , like you, am not going to hold my breath.
It wouldn’t though. because the economy will shrink, so the money we’re paying to the EU will just cease to exist, and be joined by even more. I understand we’re ‘nett contributors’ but that ignores the benefit to the economy that being an EU member gives us. It’s like making a massive saving on your rent, if you can just ignore the fact you’re now homeless. Brexit is already costing the UK economy more money than we ‘send’ to the EU.
So in other words, areas like Barnsley would be better off if we stayed in the EU Pity the silly bu66ers voted to leave.