If you are registered as self employed and have other self employed earnings and are doing a tax return and raising them invoices then its fine but the vast bulk of UK workers do not do tax returns - they are taxed through PAYE and any "employer" wanting to pay cash sounds like they do not want to give you any of your legal rights
It's not a choice. The question is whether you're an employee or whether you're self employed - that's a matter of law, not preference.. That is a decision that your employer has to make and they bear the consequences if they get it wrong.
You (or your employer) can follow through HMRC's employment status indicator tool to decide whether you're an employee or self employed.
If you're an employer, they should pay you via PAYE. If you are self employed, they pay you direct and you have to register as self employed with HMRC and submit a self assessment tax return each year, regardless of the amount of your earnings - anything over £1 and you have to register and complete a tax return, even if there's no tax due.