There is no need to correct the registration form. You would merely declare the income on the appropriate supplementary pages (SA106 Foreign) and the split year treatment on SA109(Residence, Domicile & Remittance). Any other information can be included in box 20 of SA100 (tax return). The tax return and supplementary pages can be download at
Self Assessment tax return forms
Please note that you cannot use the HMRC online tax return to submit residency information. Instead, if you have a government gateway user ID and password, you can opt to purchase a commercial tax return with the residence section included and submit the commercial version using your government gateway user ID and password.
You can register for a governemnt gateway user ID and password at:
HMRC online services: sign in or set up an account