The swap that looks close
double wall is the usual substitute for single wall boxes, and it is the wrong one. Double wall is the stronger board, manufactured in the UK, for heavy, valuable or fragile goods and for a stack. A bigger single wall box is not that board.
Packaging Boxes lists Single wall boxes separately because the jobs diverge as soon as the goods are on the bench.
What the right line actually does
Single wall is the everyday board: strong, affordable and versatile, for a normal dispatch weight.
The single wall range is the general cube. It is not the double wall range, and it is not a postal format by itself.
If you have already mixed them
Sending a heavy item in single wall because it was the size you had is how the board gets the blame.
At Packaging Boxes, Single wall boxes does not change the cutoff. Orders by 3pm leave the same day. Under £50 ex VAT the delivery is still available. It is just not the free threshold.
Open Single wall boxes when you already know this line. Bundles have a quantity. Read it before you order one bundle and expect a hundred. Packaging Boxes will still dispatch an order placed by 3pm on the same day.