You live in London and you get away with paying less than a grand a month in rent or mortgage?! Blimey. At least you're lucky in that respect.
As for childcare.... look at all the options carefully. If you have really early starts or late nights, then a nanny may work out most cost effective.
When my children were at nursery, it technically opened at 8.30 which was useless to me as teacher, as I started work at 8. I came to an agreement that they would open earlier and charge me double time until 8.30 am. Worth looking at that. A childminder is more likely to be flexible, but again, may charge extra for early starts.
Weigh up whether you're better off taking a longer maternity leave, to cut down the years your child will spend in pre-school care.
Children now get a certain number of free hours from age 3 which must be a big help.
Finally, accept that this period of your life may mean working for no net gain, for the sake of staying in your career. Many of us have been there - it is tough, and you have my sympathy, but the long term benefits outweigh the short term poverty!