I'm afraid that most employers will insist that your pay is paid by BACS into a bank account. Most companies these days wont want to be messing around with cash or writing cheques. Of course, it doesn't have to be your own bank account, you can get your money paid into someone elses and then ask them to withdraw it in cash for you.
Not having a bank account will also probably affect any credit application you make, even a mortgage.
You don't have to have one but it will probably go against you if you don't in the longer term.