I wouldn't be leaving the workplace, but based on the information you've give us, I think it's a realistic possibility that one or both of you going down to 4 days wouldn't make you any worse off.
You said you're only left with £400 a month after nursery fees. That sounds like even though you both work and you're the higher earner, you're deducting childcare from your salary alone. If the nursery place is perhaps £1200 a month, that's about average for London isn't it, that suggests you're not a particularly high earner. £1600 a month after tax, student loan and a few quid in pension is what, 25k or so? And your DH is on even less. The 5th day of the week is always the worst paid because that's the one you're paying full deductions on.
If you're on 25k paying student loan and 3% pension, and you went down to 0.8 FTE, you'd lose about £240 a month for dropping that day. I bet your childcare and transport for that extra day rushes you more than that. If DH earns less than you then it's even more likely that he's losing money by working the 5th day. There are pensions to consider too, but I suspect at your age you're on defined contribution not benefit...
With that in mind, in your circumstances I would be considering the possibility of one or both of you dropping a day at least until the free hours kick in. There's the issue of career progression to consider as well, and only you know how dropping hours would be seen in your line of work. If it's going to leave you with a target on your back then maybe not. But something to think about.
Also to be quite honest, speaking as a middle income professional in the north who lives very comfortably, I'd advise anyone who's a moderate earner in the London area to critically examine whether they really need to be there. If you love the city and lifestyle enough to compensate for the housing situation and cost of living, fair enough. Sounds like you don't though?