@Ross at Play
Actally ... as SB noted, the site you suggested is rubbish ...
Actally ... the site you suggested was a revelation!
My apologies for being dismissive before reading it carefully.
It cited 8 (in)famous quotes (4 each from both sides) by people claiming the use (or not) of the Oxford comma was creating (or preventing) ambiguities.
After considering those quotes, I have become a committed adherent to benefits of using the Oxford comma.
Firstly, the expression does NOT indicate it's the preferred style in Britain. In fact, the reverse is true. The name comes from the fact that Oxford University (or perhaps OU Press) was one of the few institutions in Britain has insisted for some time it be used.
I am going to start using the other expression for this style, the 'serial comma'.
The serial comma is used widely in the US (but not in newspapers). The non-serail comma is most common in UK (but not at Oxford).
To me, the choice is quite simple. The serial comma allows creative writers more flexibility in the meanings they can convey. It never (based on an analysis of the infamous quotes cited) CREATES ambiguities -- provided it is used correctly.
Almost all of the examples quoted, by both sides of the debate, were not actually ambiguities created by the use or not of the serial comma. Mostly were simply sentences in which ONLY commas were used for punctuation, despite the need for more than one type of separator in those sentences.
There are other separators that may be used freely when needed (semi-colons, dashes and parentheses). If the writers of the suspect sentences had used commas for one purpose (a list of items), and anything else for separating clauses, then all potential ambiguities disappear.
My example sentence ...
'She took a photograph of her parents, the President and the Secretary of State.'
I am hoping to see sentences like that quite often over the next 9 years, and I will KNOW if the writer is using serial commas, the photographer could only be Chelsea Clinton!
Writers NOT USING serial commas will have difficulty conveying that meaning. The only easy way I can see they could achieve that is by inserting 'own' before the word 'parents'.
Writers USING serial commas will have two options:
(1) 'She took a photograph of her parents, the President and the Secretary of State.'
(2) 'She took a photograph of her parents, the President, and the Secretary of State.'
There is NO AMBIGUITY with either of these sentences!
Sentence (1) can only mean Chelsea Clinton took a photograph of two people.
Sentence (2) can only mean someone, whoever they may be, took a group photograph of four people.
(I ask the forgiveness of the LGBT and other communities in presuming all people have two parents. I'm trying to make an important point here!)
IMHO, the serial comma should be preferred by creative writers, because it allows greater flexibility of meaning to be conveyed without the need for extra words to prevent ambiguities. It appears to have the benefit of already being used more frequently, by most in the US and Canada, plus minorities elsewhere (that are probably growing).
I note that both forms are correct, and both are used on both sides of the Atlantic. It is a matter of personal choice, and for your readers being consistent and accurate in whatever choice you make is more important than which you choose.