Online grocery shopping is a must
Set up all the bills you can onto direct debit so that there is nothing to action
If you and DH have access to a subsidised canteen at work, then eat your main meal of the day there - then you don't have to cook much more than some soup in the evening
If not, then rather than batch cook (although its great to have some meals ready in the freezer for emergencies), meal plan so that either of you know exactly what is going to be cooked that night, and it helps make sure your grocery shop is sufficient. I'd much rather spend 20 minutes cooking after DS is in bed than hours at the weekend - which is very precious time (he has a cooked lunch and a tea at nursery, so needs very little to eat in the evening)
Again, with cleaning - apart from the hoovering, we try and do a little everyday so that it doesn't eat into the weekend. So the one who is cooking will whizz round the sides and sink whilst it is cooking, other does the bathroom after putting DS down.
Make sure jobs are really divided equally
If you use Outlook at work, put all birthdays/anniversarys etc in your calendar, and put a reminder on them for a week before.
Stockpile some cards for when you forget
You can do Amazon Prime for 35 quid a year which gives you free next day delivery on everything. And they do an amazing range now - so it gets you out of a lot of holes !
And most of all, accept that you will not do everything perfectly, and that sometimes something has to give. Don't be ashamed to outsource stuff if it makes your life easier