Scholarships and Bursaries
Most schools offer both merit based Scholarships and means related bursaries. It's rare to find a full fees paying Scholarship these days, but some are still offered. Schools will now mostly offer either one or two top scholarships of up to 50%, together with perhaps half a dozen lesser awards from 10% to 40% of fees.
Scholarships are usually awarded as a result of both tests and interviews. Most schools automatically consider every pupil for an award on the basis of their entrance test performance, and then invite selected pupils back for a specific scholarship exam. Non-selective schools will usually write to prospective parents to advise them of the existence of the scholarship scheme.
Bursaries are usually awarded as a result of both pre-qualifying criteria such as a parent being in the Armed Forces and an Old Pupil of the school, and as a result of means testing on parental income. Schools regularly offer up to six bursaries a year, generally in the order of 10% to 25% of fees.
Your best source of information on how to apply, and eligibility criteria, is always the awarding school, so do pick up the phone, ring the headteacher and admissions secretary and speak with them about this.