While you can't get a DBS (formerly CRB) check for yourself, your local police force is obliged to provide you with a copy of all of the information that they have about you (except, of course, where an ongoing investigation prevents disclosure) if you simply make a 'subject access' request, provide proof of your identity and send them a £10 fee. That effectively tells you what a DBS check is likely to show. (Google "subject access" "xxxxx police", where 'xxxxx' is the name of the relevant force, for information about the procedure).
The rules about cautions have been changed several times. One of the main reasons that they were introduced in the first place was that they offered a way of dealing with minor offences that did NOT create a criminal record for the offender. However, as soon as the CRB came into existence, the whole principle was undermined by them being included within CRB checks.
To complicate matters further, police originally had discretionary powers to delete cautions from the database after a certain period of time (which was usually 5 years). Some forces used their powers, while others did not, so that whether a caution remained on record was a lottery based upon where you live.
Then a UK court ruling removed the discretionary powers from police so that all cautions remained on file for life (but those which had already been removed weren't reinstated).
Now a Court of Appeal judgement (based upon the European Convention of Human Rights) means that some cautions will be removed from the records after 6 years. However many politicians are campaigning for the UK to withdraw from the ECHR, so there might still be further changes to come!