It is not against the law to pay someone in cash, but you cannot pay someone “off the books”. Many people assume that it is all right to pay a cleaner a relatively small amount every week without paying tax and NI, or to pay someone for a few days temporary work, but it depends on the circumstances.
Casual workers do not have a continuing contract with the organisation to provide work. Strictly speaking, casual workers are those people who work for your organisation for less than a week. Even then the PAYE system must be operated for casual workers unless their earnings are below the PAYE and NI thresholds and they have no other taxable income. A record of their name, address and total pay must still be kept. If they are subsequently kept on or it is agreed that they will work for you again in the future, it is necessary to complete a form P46 and return it to PAYE office.
Form P46 asks a few basic questions of the employee, including a question about other employment. If a new employee does not have a P45, then form P46 must be completed, and sent to the tax office.
So you could pay your cleaner £40 a week without deduction of tax and NI if they have signed a P46 confirming that they have no other job because this is below the tax threshold. And you can pay your temporary worker without tax if they only earn less than the tax threshold in the week.