Not sure. A good lot of us in this family are good at English and I suppose that's about reading books. If you read and read and read all day long you tend to get good at English and that does not require a huge amount of teacher input.
There are two issues here - some of these children on the programme are very clever and separately they prepared and swotted for the competition. Normally they would just be reading or studying for their own fun into subjects in which they were interested or for an additional early GCSE or A level. I don't think the fact the parent sat them down and spent some time for the competition coaching them in their special subject necessarily reflects the parent/child teaching going on outside of the programme although that will vary from family to family.
I have always thought this kind of thing is about 50% nature and nurture - indeed for all of us.