There is a possiblity that penalties may be applied.
You can estimate your Self Assessment penalties here:
Estimate your penalty for late Self Assessment tax returns and payments.
If penalties are applied, you can appeal them, provided HMRC has all of your tax returns.
You can find guidance which will help you submit appeals against late filing and late payment penalties here:
Disagree with a tax decision
You are unable to appeal against interest charges on the late payment of penalties on outstanding tax. You can, however, object to the interest charges. We would only consider your interest objection when all tax liability is paid.
You can raise an objection by phoning or writing to HMRC.