It may depend on exactly what information the landlord wants from your bank statements. Apart from proof of income, the landlord may be interested in you bank balance as evidence of your financial status. The landlord my also be interested in any regular payments.
It may be to your benefit, to ask what information the landlord wants from your bank statements, letting the landlord know that you will provide additional documentation for any required information that is not on your bank statements.
It may also be in your interest to find out what information the landlord is legally entitled to ask for and receive. If the landlord is asking for information to which they are not entitled, that does not necessarily mean that you should not provide it.
An optional proof of income would be any documentation for receipt of your cash income, such as a receipt. If you don't provide or keep any documentation, now is the time to start! You could also deposit each payment into you bank account so that it will appear on your bank statements.
In lieu of any cash receipt documentation, you could approach the organisations that have paid you in cash and request a statement identifying the amount(s), date(s) and the name of the organisation for each payment. This could be in one document for each organisation.
If any organisation declines to provide the requested documentation, and you need the missing evidence of the additional income, you could get your accountant/tax agent to provide a statement of income. Which would be preferable to providing the landlord with a redacted copy of your income tax return, or an extract thereof.