(2 part post):
The people who work with troubled children are usually educational psychologists, rather than psychiatrists but I'll try to give you information about both psychiatry and psychology:
Psychiatry is a specialist branch of medicine, so you have to qualify as a doctor before you can become a psychiatrist. To get a place at medical school you'll normally need a minimum of an A and 2 Bs at A-level. The subjects must include maths and 2 science subjects. (NB: These are the absolute minimum requirements. Many successful candidate often have 4 A-levels, all at grade A).
It's also possible to get into medical school with exceptionally good A-level results which aren't in the above subjects but, if you do this, you have to take a one-year pre-medical course first.
Your medical degree will take 5 years if you entered by the first route above or 6 years if you need to take the pre-medical course.
You'll then start work in a hospital while undertaking a 2-year foundation programme. Half-way through this programme (i.e. 6 or 7 years after you started training, you'll become a 'proper' doctor registered with the General Medical Council).
During the 2nd year of the foundation programme you'll be able to start moving towards your chosen medical speciality (i.e. psychiatry).
After you've finished the foundation programme, you'll continue combining work with training for five or six years.