Ok so I was curious about this and I apparently have nothing better to do so I have just tested it on the Asda app.
I went in and had nothing in my basket and no delivery slot booked. Basket shows as zero.
I booked a £5 delivery slot and it added £5 to my basket in the top right of the screen.
I then added a whole chicken priced £5.44. The total in the top of my screen went to £14.44, apparently adding the minimum basket charge on.
However, tapping on the basket doesn't bring up the basket plus charges, it only shows you what you have, in my case a single chicken, and no explanation of why that chicken is going to cost £14.44. It's not until you tap on 'check out', then tap on 'continue check out', and then scroll down a whole two screen lengths, that you get to the order summary and there the totals are line itemed out.
So next to my chicken I added two lego kits which together come to £31.94. My basket is now showing as £46.38. Great thinks I, that's a £40 basket plus the £5 delivery charge (because maths is not my strong point). But no, of course it's £37.38 plus £5 delivery and £4 basket charge.
Adding three bags of apples at 99p one at a time takes my basket to £47.37, £48.36, and then £45.35. Which actually is a £40 basket and a £5 delivery charge.
I agree OP that it is not clear or user friendly. If I was designing this, when you tapped on the basket to see the shopping contents it would also display any charges such as the delivery and minimum basket charges. You shouldn't have to go all the way to checkout and scroll all the way down the page to get that information. It's way too much of a faff. I would write to them and complain if I were you. Tell them to sort their UI out and remember that people are trying to save money and shop smartly here and they are making it more difficult.