The English and British governments, being agents of both bureaucracy and imperialism, and these two things being far from separate, produced a considerable amount of paperwork concerning their empires. Various collections and calendarisations have been made of this:
British History Online has, in fully transcribed and free to view text, the 41 volumes of the Calendar of State Papers Colonial covering America and West Indies, 1574 – 1739, and the 5 volumes of the Calendar of State Papers Colonial covering the East Indies, China and Japan, 1513 – 1634.
British History Online also has the 14 volumes of the Journals of the Board of Trade and Plantations, 1704 – 1782, again fully transcribed.
The Acts of the Privy Council, Colonial series, are to be found on Hathi Trust, Internet Archive and Google Books:
Vol. 1, 1613 – 1680: Hathi Trust. Internet Archive.
Vol. 2, 1680 – 1720: Google Books. Hathi Trust.
Vol. 3, 1720 – 1745: Google Books. Hathi Trust.
Vol. 4, 1745 – 1766: Google Books. Hathi Trust.
Vol. 5, 1766 – 1783: Google Books.
Vol. 6, 1676 – 1783: Google Books. Hathi Trust.
There are also various volumes of material relating to colonial governance, many collected together by U.S. scholars.
British Royal Proclamations relating to America, 1603 – 1783: Internet Archive; Gutenberg.
Proceedings and debates of the British parliaments respecting North America (6 vols): Hathi Trust.
A useful bibliographic volume, though the documents are now to be found at the National Archives in Kew, rather than the P.R.O., is:
List of reports and representations of the Plantation councils, 1660-1674, the Lords of trade, 1675-1696, and the Board of trade, 1696-1782, in the public record office: Internet Archive; Library of Congress.