If you need to advise Companies House of a change in the SIC code you will have to file a Confirmation Statement.
The only way to update the SIC code stored at Companies House is by filing a Confirmation Statement.
How Do I File a Confirmation Statement? (CS01)
Why Might I File a Confirmation Statement Early?
You must first update the SIC code that is stored on Inform Direct.
Note: Until you file a Confirmation Statement, Inform Direct will keep a record of your updated SIC code on the system. So, when you next file your Confirmation Statement, your SIC will be updated automatically.