I'm in a simmilar position to you, op, except that I have 4dds. I'm in central London, no familer support (they are all half a world away!), a sahm mum and dh works long hours. Adding to our mix is that we are slowly doing up a house! Dds are 5, almost 4, 2 and 4 months.
I don't do all the housework, it just doesn't get done!!! I keep the ground floor reasonably tidy, upstairs is another matter. Downstiars can be completely trashed in a couple of hours when dd4 just wants to feed. May take a couple of days to get on top of it - i pray we have no unannounced visitors in that period! I could do with a cleaner, however, not worth it until we get the bathrooms renovated. I've had cleaners before and I am busy cleaning before they arrive!
Dh pulls his weight a lot more now and is very active with the kids. Also better around the house, and I cannot really complain!
My girls do gymnastics, it is a logistical nightmare. I take all my four plus buggy and scooters. It is hard entertaining them all while the other is in their class (two seperate classes for the two oldest). My oldest does tap as part of an after-school class, that helps a lot, and dd2 will be able to do it in Sept also.
I second come of the comments of sharing school runs. I have three different school runs to juggle (urgh) and I need a car to do some of them. I also help out others when I can, and I now have a couple of people I can get to help me (like this week when our car failed its MOT).
It's hard, really hard. There are not many around me (well, only a couple of others and I do not know them well) that have four, and so close together). It's hard to arrange playdates for all of them, and dd2 is kind of jealous of dd1 being at school (roll on Sept!).
I guess routine is a great help, but with dd4 still only four months, the routine is only just sorting itself out.I have a rucksack full of pencils, paper, toys and food (and nappies and wipes!), that helps also. Good luck!