The idea
There are many illegal immigrants who have entered the UK and been living invisibly and working on the black economy because they do not have official documents. I believe there should be an amnesty window, and those who are living underground as it were, could buy their citizenship by paying a very large fine for the illegal entry, which could be spread over some years like the student loan system. As someone with the status of a probationary immigrant, they would be allowed to work legally and contribute to the economy, and also pay a higher tax rate for a while to compensate for the years they could not pay tax, as we have no way of knowing or proving what they earned or how they survived during the time they were invisible.
The probationary citizen period would end when the fine was totally paid off. I would suggest the figure shoudl be around 12-15,000 per person. Once they are working legally, deductions could be made at source at a rate that is deemed managable so they do not suffer hardship, or the fine scheme be too offputting.
Why is it important?
This applies only to those who have been living here for some time and can prove that. They are invisible, yet they often benefit from our healthcare etc by using the identity of realtives and going to doctors who do not know them, The invisible and hidden immigrants are not currently contributing to the economy, and if they cannot legally work there is a higher risk that they will support themselves through illegal activity. If they are given a chance to come clean, then we can tax them and they can contirbute to society and stop living in fear.
A probationary period and a non-criminal "fine" enable them to buy their right to remain. Exemptions will apply. If a person has a criminal record for example, they would not be eligible. They must be willing and able to work legitimately for teh duration of the probationary period, and the full benefits of citizenship would nto be avaialble to them until the fine is fully paid. A low interest rate will apply.