You don’t have to have a written complaints policy or a returns policy or process. Even if you do have a complaints policy there is no obligation to publish it on your website, but some businesses use it as a way of demonstrating their ethical trading.
However if you publish such policies you must make sure that they do not have any restrictions that may take away consumers statutory rights as these terms would be illegal. Similarly a blanket ‘no refunds’ notice in a bricks and mortar shop is likely to be illegal. It does not help to include the phrase ‘this does not affect your statutory rights’.