I'd ignore the instruction.
I use an Oxford comma when it would be clearer or more elegant to use the Oxford comma, otherwise I don't.
I suspect that anyone else who cares enough about the Oxford comma to have learnt that that's one of its names has their own preferences too, and would know that even if somehow letter-writing style were the most important issue for the NHS to tackle right now, effective writing isn't about blanket rules on the Oxford fucking comma.
Maybe this is one of those broken-window things 