Good behaviour over time doesn't get you a clean sheet in the UK
Some countries want to get a copy of your 'rap sheet' which is handled through a related organisation to ACPO - the unofficial body that governs police activities.
There is one type of record specifically used for Australia, Canada, the USA and a couple of other countries. Even though a persons criminal record might have been expunged through a period of 25 or 35 years good behaviour, these 'clear records' actually contain information that alert the aforementioned countries that the person actually has a conviction history.
Police clearances for other countries are essential a request by the applicant for a copy of the applicants own police record which INCLUDES EVERYTHING, even though technically expunged. This of course makes the whole exercise pointless, if you are trying to show you have a clean record.
In Canada the clearing of a criminal record is handled by the Parole Board and when it says an applicants record is clear, the applicant can get a really clean report - although any offences remain on record in a partitioned area on the computer and can only be released after a proceeding - usually caused by a persons return to their bad ways.
BTW, the U.S. immigration people have a neat question: "Have you ever been arrested?" An affirmative answer opens the door for further questioning. If you lie to a federal U.S. official you commit a felony - the serious type of crime!