It can be more tax efficient to file tax paperwork, but I don't want to do paperwork, so I just had an umbrella employ me when somebody insisted on hiring me as a "contractor" and the umbrella handled the paperwork for which of course they keep a fee. As far as the government is concerned I just had two PAYE employers, the umbrella and my "real" job.

Having multiple employers also does not require filing taxes. One of the employers gets given a zero tax code and they tax all your pay at full rate, the other one gets a normal tax code which reflects your personal allowance and other considerations. My tax code was oscillating all over the place - but that's not a problem it's all automated.

If you love paperwork you can choose to do all the paperwork. Or if you love money and don't hate paperwork maybe you can save a few hundred quid by filing and I hope it makes you happy. I hate paperwork, and I have plenty of money. So, no, despite earning a lot of money and having worked as a contractor I preferred to stick with PAYE.

The HMRC will take a fair cut of my gross income, which is fine, and then leave me alone whereas an accountant earns money by bothering me with more paperwork.

How do you know it's fair?

Accountants don’t bother you - once a year they ask you to sign your accounts.