Benefits in kind are non salary benefits which are taxed in the hands of an employee or, in the case of a limited company, a director. Any employee, whether they work for a limited company or a partnership, is liable to taxation on a benefit in kind. Obviously an employer who is not a limited company does not have directors but this then can make it difficult for a proprietor, e.g. a sole trader, to get an aircraft's operating costs allowed as an tax deduction when assessing the taxable profits of the business. The difference in treatment of a director arises from the fact that a director is a separate legal personality from the Company of which he is a director. This consideration does not apply to unincorporated bodies, such as partnerships. Some of my staff get taxed on benefits in kind, though I do not trade through a limited company.
I don't believe you can have a BIK charge arising unless you are an employee (or director). I suspect that for it to arise with a director they also have to be an employee - most directors in small companies are also employees of the Company.