I only found support for the idea that Sanskrit is the ancestor of English
That's strange. See, for example, the wikipedia article on the 'Out of India theory', which clearly states that 'This theory is deprecated in mainstream scholarship'.
Update: I found that there is actually a wikipedia article about The Adventure of English, the TV series upon which Lord Bragg's book (which you cite as your source above) was based. Here's an extract:
Critics of the programme have pointed out that it contains factual errors: for example, it asserts unequivocally that the Indo-European languages stem originally from India