You mentionned 2 points:
- police not involved
That means there is no criminal record of the misuse / misconduct
Access to the DBS checking service is only available to registered employers who are entitled by law to ask an individual to reveal their full criminal history (ref: Disclosure and Barring Service)
The Disclosure and Barring Service (DBS) helps employers make safer recruitment decisions and prevent unsuitable people from working with vulnerable groups, including children. It replaces the Criminal Records Bureau (CRB) and Independent Safeguarding Authority (ISA).
Unless you have to deal with children or vulnerable group (ref: Disclosure and Barring Service), or seek for a high-level position related to financial/security matters (ref: Wikipedia / DBS), your previous 'mistake' will not affect DBS as it's not related to this.
As @Dan mentionned it, it's also not about 'employment history or financial status'.
Internal / private disciplinary action IS NOT legal action.