The previous expert has decided to opt out.
After reading through your interaction I would like to suggest that you make a complete declaration and as soon as possible.
You first need to seek a local tax professional because you will need to start at the local tax office.
If you have undeclared income, you have broken the law and, from HMRC’s point of view, are guilty of tax evasion.
This means that HMRC can prosecute, but will normally only do so in cases which involve fraud or false accounting.
When you have substantial undeclared trading income over many years you should take the first steps and approach a local tax office.
The tax office will pass your case to an inspector. The inspector will also normally want tax returns completed for all the years concerned. This is why you will want professional assistance.
Once this is all completed the tax will be expected to be paid. If you cannot pay HMRC may allow you to pay on time.
You asked for an official form or example. The form is the tax return completed. If you disclose your income (by completing returns for the years in question) and cooperate fully with the investigation or enquiry that will follow, this should help to reduce any penalties payable.
As to how long the process will take, that is not possible to know.