See, if the OP and his wife have a house in Holloway which they don't have to pay for, I think that they should be able to afford, even on one wage to have a child in nursery a but, say 6 hours a week.
Housing costs are so massive, espeically in London, that that must free up some money.
I don't think it's fair if OP's wife won't discuss the matter, of course it's not.
But, he is coming over as rather nasty.
If I do reverse the situation, and I think, OK, I am a working mother, with a 16 month old baby and no mortgage.
My Partner is at home with the baby all the time, except for two hours a day. I come home to, presumably a clean house, with the laundry done, the dinner made (in London few working people get home before 6 pm),the shopping done etc, I really don't think I would resent that.
In fact, I would bloody love it! (Where so I sign?!)
OP's attitude to looking after a child in general is a bit odd, and it strikes me that he may never have done it himself for a whole day.
If my fantasy partner did spend some of his time having coffee with other parents of small children, and going to the park, then great! I wouldnt want my partner to be miserable and without friends.
Imo, it the lack of communication about this that is the issue, not the money.