This Act excludes Scotland from its provisions, but it has an effect on Scottish public records in two respects:
With the agreement of both the UK and Scottish Keepers, UK public bodies operating wholly or mainly in Scotland may transfer their records to the National Records of Scotland rather than to the National Archives (TNA) which are based in London. This is made possible by an interaction between section 3(8) of the 1958 Act and section 5(1) of the Public Records (Scotland) Act 1937.
In 1962, the Scottish Office adopted the arrangements for access to government records set out in the 1958 Act and also adopted similar arrangements for the selection, transfer and preservation of government records.
You can find more information about the 1958 Act in the policy and legislation section of The National Archives (TNA) Website.