The National Archives maintain available Privy Council records as far back as the Fourteenth Century, which is the closest you'll get to 'official' records from that time. However, your question seems to assume that modern government record keeping, bureaucracy, and secrecy are ancient traditions. The fact is, that things like public or classified documents didn't exist back then. Privy Council records, and all over documents, were more or less private property, and no one expected the government to be transparent in any way (and a lot more emphasis was placed on personal power.) Nothing was 'classified' because no documents were default open. Sure, the records are very patchy, but that's because they're mostly private notes, not an official record.

But yes, Elizabethan officials had 'secret' papers, but they were personal to the individual - not a sealed government record. We know Elizabeth I even received coded messages, but they were still personal communications. Even her spies would give personal reports, MI6 didn't exist, spies were personal employees, the Royal Navy was just ships that belonged to the monarch.