Not sure what you mean by your bolded line, as that would not be the previous day (if it was the previous day then the 0900 reading on the 2nd would count for the 1st).
Anyway I have found a (hopefully) definitive answer on the Hadley page: https://www.metoffice.gov.uk/research/climate/maps-and-data/data/haduk-grid/datasets
Maximum: Maximum air temperature measured between 0900 UTC on day D and 0900 UTC on day D+1 (ºC)
Minimum: Minimum air temperature measured between 0900 UTC on day D-1 and 0900 UTC on day D (ºC).
So that would mean that the max reading at 0900 on the 2nd would be credited to the 1st, and the min reading would be credited to the 1st. Which makes sense as usually the maximum would have been on the 1st and the minimum in the early hours of the 2nd.
Obviously it can sometimes mean that if there is a sudden overnight warmup, the max is credited to the "wrong" day, or if it is still very cold just after 9am on one day and it then warms up, the cold minimum gets double counted.
Anyway this does explain the line about there being "always one more minimum than maximum", because the minimum for today (11th) was already known from 0900Z today, but the maximum for today will not be officially known until 0900Z tomorrow. It's talking about the rolling average, because on any given day N it will always have N minima but only N-1 maxima (because the maximum for day N is only known on day N+1). Simple! ;)
Originally Posted by: Rob K