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.