our ops manual states 2 nm is OK without informing ATC.
Your Ops Manual may need updating!
From the AIP
This applies when you are Identified:
must advise ATC prior to initiating or changing an offset
In the real world, I guess this means you have to tell ATC of the offset before being indentified!
Easily confused with the next paragraph:
The decision to apply a lateral offset is the responsibility of the pilot in command.
Other than when an Identified aircraft initiates or changes an offset,
pilots are not required to notify ATC that a lateral offset is being applied