This tip is based on questions posed on the CALL listserv; thanks to John Sadler and Linda Keddy.
According to “How to look for records of … Privy Council since 1386”, a finding aid produced by the United Kingdom National Archives, royal proclamations “are formal announcements made by the King or Queen and vary greatly in nature, from declarations of war or states of emergency, to the summoning or dissolution of Parliament. … [They] were usually issued with the agreement of the Privy Council and can therefore be found in Privy Council papers.”
Unfortunately no site has a comprehensive collection of Royal Proclamations. Some, but not all, of the Privy Council records are available online through the British National Archives; you can search them at https://discovery.nationalarchives.gov.uk/advanced-search.
You can also find Royal Proclamations in The London Gazette (established 1665).
If you can’t find the Royal Proclamation you’re looking for online and it pertains to something Canadian, Linda Keddy suggests going the old-fashioned route: newspapers on microform and archive files.