This section contains various ‘private’ acts, generally classified as either local or private, passed by the English, British and U.K. governments. Some 37,500 of these have been passed since 1539. (Source: Legislation.gov.uk. ) For a pithy introduction to what these are, see Wikipedia. The majority of these acts are very hard to find; few were collected in the volumes I have been OCRing, some were never printed at all, and most had very imited distribution.
Note that although there is a distinction between Public and private acts, the latter could be declared ‘public’; see, for example, the last clause of the Lancashire Sessions Act, which states:
And be it further enacted, That this Act shall be adjudged, deemed, and taken to be a Public Act; and shall be judicially noticed as such by all Judges, Justices, and other Persons whomsoever, without being specially pleaded.
This is a matter of legal standing, rather than parliamentary procedure and classification.