Is there a law in England stating that a criminal record with minor offenses cannot be viewed over the Internet?

One can apply online now, but the resulting certificate is posted to the subject and is not visible online.

NO British criminal record is visible online. This has to be confidential information to make the Rehabilitation of Offenders Act 1974 work.

And this is why the DBS exists. Only employers who NEED to know because the job involves, for example, working with children, or it is a job as an accountant and they want to know if you have a record for fraud, are entitled to apply for a DBS disclosure.

A standard or enhanced disclosure includes all convictions however old, but a recent change to the law allows the DBS to leave out minor convictions or cautions that are old. This is probably what you are thinking of. The full rules for what can be filtered out are http://lifeyouwant.org.uk/wp-content/uploads/2013/10/dbsfilteringprocess.pdf but basically, for an adult, cautions over 6 years old are omitted, and convictions over 11 years old but only if you only ever had one, it did not result in a prison sentence, and it was not a specified offence (the link gives some examples of those).

NO criminal offences can be viewed online in the UK, due to the Data protection Act.