In the UK, secondary school education culminates in the General Certificate of Secondary Education (GCSEs). After GCSEs students can attend college and undertake a range of qualifications including A-levels and the International Baccalaureate Diploma Programme (IB). For the equivalent qualifications in your country please see this UCAS publication.

If you choose to send your child to the UK to study for their GCSEs, they can attend independent schools and boarding schools while if you your child has already undertaken their secondary education certificates they can study at independent schools, boarding schools, private schools and pathway study centres. 

If your child does not have quite the right qualifications to attend university there are many international study centres and university-run foundation programmes which offer A-levels (a top-up if they've some qualifications) or a Foundation Programme which gives students a 'pathway' to gain the necessary skills to advance in their chosen degree path. After graduating from this pathway, they will be able to continue with an undergraduate degree at the same university. 

These qualifications are then followed by an undergraduate degree, the most popular being a Bachelor's degree, which can then be followed by a postgraduate degree including PhDs and Master's.