The police retain records of arrests as 'Nominal' records on the Police National Computer, currently until the subject reaches 100 years of age. This policy is the subject of ongoing debate.
Whether the arrest will show up if you choose to make a Subject Access Request is not clear. Various Data Protection exemptions apply to the police, and arrests are not specifically included in the list of information returned under a Subject Access Request:
https://www.askthe.police.uk/content/Q87.htm
But equally nothing you describe should lead to a disclosure under a 'Standard' CRB check (you don't have a 'Criminal' record if the charges were dropped):
http://www.businessli...416048&type=RESOURCES
... and if an employer performs a CRB check on you, you will be sent a copy of the report.