double and's in list and commas

I would like to know if the following sentence is correctly written. The reason I am asking is that I write in British English so do not put a comma before 'and' (that comes before the last item) in a list. However, in examples such as the one below, each list item is a word-pair separated by 'and'. In this case, do I need to add a comma before the second last 'and' (the last 'and' is a part of the list)? Also, do I need to add a comma before 'products'?

This is why we need fruits and vegetables, toiletries and cleaning agents, and groceries and baked products at our new home.

The heated debate over the serial (aka Oxford) comma only applies when neither its presence nor its absence affect the meaning of the sentence, i.e. it’s completely optional.

In this case, it is required because if you remove it, the last two pairings fall apart and it looks like you don’t know how to build a proper list. With it, your list looks like an odd (to me) but valid stylistic choice.

I can’t see any reason why you’d put a comma before “products”.