On a more serious note, get confirmation of the exact dates you were working, in education or registered unemployed.
If you were registered self-employed at any time, HMRC can supply a letter stating the dates of when you started and stopped. From my experience you need to tell them exactly what you want.
If you were out of the country, airline ticket stubs, receipts, boarding passes and visa stamps can prove where you were. If it was for any length of time you may have registered with a British consulate, or be on another countries tax, social security or immigration system.
Any other bits, I think a referee of 'good standing' (like for a passport application) can supply a letter stating what you were doing.
Assuming it all goes OK for this application, KEEP THE RECORDS, as you'll have to do it all over again for your next pass!