Are benefits received by self-employed workers taxable?

If a business takes on a worker on a self-employed basis (assume all/ most conditions determining self-employment are met) and then provides a number of benefits e.g. provides a motor vehicle to him/her, pays a pension contribution for him/her and provides free living accommodation to him/her, are some or all or none of these benefits taxable in the hands of that self-employed worker? Assume that the total remuneration including benefits is < £8,500 pa.

Is it correct that no P11D or P9D would be required from the business because the worker was self-employed?

The follow-on question would have to be whether the self-employed worker, while satisfying all the other conditions determining self-employed status, could still be classified as self-employed after receiving benefits such as these?