The UK have a statue of limitations on most types of criminal convictions which would not show up on a Standard Criminal Records Bureau (CRB) check but may do so on an Enhanced CRB Check.
Question is would you have to declare any expired convictions?
The US did not get the access the wanted to the UK CRB records as I recall, but it was a close thing.
The US does not have the concept of a spent conviction and they do not respect other countries rules on that matter either. A CRB check with a spent conviction will just show 'No Live Trace' which tells them there is something in your past but not what it was. No conviction history comes up with just 'No Trace' as I recall.
Access to the old data is only accessible by certain people and only with very good cause.