I completely disagree with advice that says stop going to baby groups so that you can keep on top of the housework!
Why on earth should anyone with a 4 week old baby deny herself opportunities to interact with other adults, including those in a similar situation to herself, on a daily basis whilst hopefully building up a local support and friend network to sustain her through those early years in order to do the ironing?
At 4 weeks, my babies were feeding constantly and dc2 in particular took HOURS to persuade to sleep in the day so that she'd stop screaming with tiredness...
I often did manage to cobble some evening meal together, but it was at the expense of me resting or doing anything positive for myself, which I wouldn't recommend to anyone else.
It will get easier OP, but it sounds like your dh and you need to rework the division of labour and expectations. If he insists on meat from a butcher, maybe he could do the meat shop on a Saturday morning, for example?
It's hard when there's been a bit of a domestic bliss thing going on whilst you're on mat leave in late pregnancy, then all hell breaks loose at home once the baby is here!