Question to the Home Office:

To ask the Secretary of State for the Home Department, which criteria are applied by UK Visas and Immigration staff when judging a visa application to be non-straightforward; and what service standards govern the (a) processing of such applications and (b) updating the applicant on the status and progress of their application.

Visa applications are considered to be complex when an Entry Clearance Officer determines that additional information is required in order for a decision to be made.
There are no set standards for processing non-straightforward (identified as complex) by the caseworker. However, if an application is complex and expected to take longer than the standard processing timescale, UKVI will write to the customer within the standard processing time and explain what will happen next

The published information on processing times for visa applications is published as part of the Migration Transparency data, available at https://www.gov.uk/government/collections/migration-transparency-data#uk-visas-and-immigration