The 31 January is not just the final date for submission of your Self-Assessment tax return but also an important date for paying tax. It is the final payment deadline for any remaining tax due for the 2018-19 tax year and any payment on account due for 2019-20.
If you miss the filing deadline then you will be charged a £100 fixed penalty if your return is up to 3 months late, regardless of whether you owed tax or not.
If you do not file and pay before 1 May 2020, then you will face additional penalties and interest. A daily penalty of £10 per day, up to a maximum of £900 (90 days) will be charged from 1 May 2020. Further penalties then apply if your return is still outstanding for more than 6 months after the 31 January filing deadline. From 1 August 2020 you will be charged a penalty of the greater of £300 or 5% of the tax due. If your return still remains outstanding one year after the filing deadline, then further penalties will be charged from 1 February 2021.
You can appeal against any penalties that have been issued and HMRC has said that they will treat those with genuine excuses, leniently. However, you need to act fast and the excuse must be genuine and HMRC can of course ask for evidence to support any claim. An appeal must usually be made within 30 days of receipt of the penalty.
If you do not have the necessary funds to make payment you should be pro-active and contact HMRC as soon as possible. Pretending the problem does not exist will not make the problem go away and will likely make matters worse.