Personally I would not make any decision in haste, you have plenty of time to do this, but if you rush it, you run the risk of taking on an awful lot of overheads, expenses and stress whilst potentially having a very low income stream at the beginning.
I don't know about the legalities of basically pinching existing customers, I would make sure you are compliant in all aspects of the law and GDPR. There is a date by which you have to register for self assessment, so it is not something you have to do straight away, I believe its 5th October for the last tax year, so if you were to start trading today, you would need to register next year. If you keep a separate account for your income and expenses and just transfer your income to your personal account, most accountants will work off the bank statements, as it is then quite easy to see what has come in, what has gone out, and what is drawings/profit. From day one your going to need liability insurance and business car insurance, and money for stock, products etc.
Would it be better to try and find a salon that engages you as an independent, and you split the profit with them, whilst you build your business up slowly, being bald, I am not sure how these things work, but I do know that a steady income stream does no harm whilst you transition from employed income to self employed income.
For the moment, accept your employer is a moron, and start looking for another job, once you have another job where your work ethic and skills are accepted, and they charge a reasonable amount and pay you a reasonable amount, then start looking at how you can work for yourself and build up a business from scratch in your own time.
2 links you may find interesting, I would point out that although your employer is clearly a moron, there may be legal, and certainly moral issues with stealing customers, you sound good at what you do, and certainly good enough to be successful without resorting to something that could be illegal or immoral, word quickly gets round, if your good, you will do fine!
good luck,
How to Start Up Your Own Mobile Hairdressing Business %%sep%% Le Salon
A former employee has stolen my customers and is targeting my staff, what can I do about it? - Acumen Business Law