You can say you are an escort on your tax return. It’s legal therefore HMRC wouldn’t give a toss.
No one from the general public can have access to your tax return and it would be very limited few that could access it.
When applying for a mortgage and any other loan, credit etc, they do not see your actual tax return. They see a document called a SA302 which just confirms your income, tax and NI paid
For example, you could put Escort on your tax return and tell your mortgage company that you’re a hairdresser. This would be lying but they would have no way of finding out through your tax return.
If you want to be more broad on your tax return you can state that you’re a ‘Therapist’
I’m just buying a house and I’ve had no problem

As for your accountant knowing your personal details, I wouldn’t worry as long as they are of a professional body they are obliged to keep your information private.
All accountants charge differently and it all depends on what you need them to do.
I paid £300 for an accountant to submit my tax return and never again. I do it myself online for free. Just keep a simple log of income and expenses.
Self assessment only want to know those two figures, they calculate the rest for you