On relatively low salaries OP and paying for childcare, it's possible you won't have much/any less money coming in if you both drop a day, maybe even two. Especially DP. Reason being that because of the way tax works, your 5th day of the week is the worst paid. Whereas people who earn less keep a higher percentage of their wages. And the personal allowance, what you can earn before paying tax, is quite high at 12.5k. So it makes sense for you both to earn enough to use your full allowance.
So if your childcare costs the same each day, it's possible that you will earn enough to be in profit on your first 2 or 3 days, where you're effectively only paying NI, but not on the 4th and 5th days when income tax kicks in.
For example on 21k the take home is is £1484 per month without pension or student loan. If DP does 4 days a week at this rate, it's 16.2k annually which is £1212 per month. So £272 less for dropping a day, which some people would have to spend around that for the 5th day of childcare and commuting costs anyway. On 3 days a week, 21k pro rata is £12,400 per annum is £995, which is £489 less than you'd get for full time.
If you have cheaper childcare and/or commuting costs, it may still be more profitable to work full time. And you'd want to factor in any help you might get from tax free childcare plus impact on pension. But if your combined childcare and commuting costs are more than £55 per day, which many people's are, it doesn't necessarily have much impact on your pay packet to drop a day or two on a modest salary.