OP appears to have done virtually no research on medical careers in the UK at all, which is rather worrying for an alleged to be riding 17 year old currently in year 12.
Psychiatry is a Medical Speciality, to practice as a psychiatrist one Must be a Registered Medical Practitioner
In the UK there is not a division between 'state' and 'private' Universities like there is in the US,
In the UK Medicine is an Undergraduate Programme, unlike the US, theroefore one applies ot Medicine as a Undergraduate degree.
I strongly suspect that the OP is not going to be a strong candidate for any Pre-reg course within the next year regardless of academic achevements.