I can see no reason why you would not be permitted to enrol a young person where there is no government funding, but you will need to consider parental approval and safeguarding as for any young person.
The question is then how to include in the ILR as only aims that are 16-19 funded can be put against a learner who is under 19. If you try any other non-regulated non 16-19 funded aim, it produces an error in the FIS.
I’d be interested to know what aim we should use etc.
I have always believed that one cannot charge an under 19 for anything (on pain of losing your E(S)FA funding). I think it is acceptable to invoice the employer of such a student and possibly a parent.
You are correct regarding delivery to those 16-18 during the academic year but summer school provision between the end of term in July through to the start of the next academic year is not funded by the ESFA and where provided by a College or Training Provider can only be charged as full cost.