Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
Are you referring to penalties for late filing of tax returns or late payment of tax liabilities? How many tax years are involved?
Leave this with me while I draft my answer.
If you file your tax returns late, you are subject to a penalty depending on how late the returns are submitted. The penalties for the 2014 and 2015 tax returns can be found here.
If tax returns are late, invariably the tax liabilities arising from those returns are paid late too and, therefore, the taxpayer has gained an advantage over those who completed and submitted their tax returns on time and paid their tax on time. If no tax is due, the penalties are harsh but they are in the public domain so nobody can plead ignorance.
You can appeal against the penalties but you need to have a reasonable excuse in order to have any chance of having the penalties cancelled. Some examples of reasonable excuses and excuses that don't count as reasonable can be found here. The appeal from can be found here. If your appeal fails, you can apply for a further review and if that fails you can go to an independent tribunal.
I hope this helps but let me know if you have any further questions.