The programme doesn't appear to be available on the web site, but there was this in a press release about programme's from a year ago it seems (on this page):

"Presenter Robert King attempts to discover the origins of the National Anthem in Anon's Anthem (Tuesday 4 June, 1.30pm). Scholars now tend to believe the anthem in its first manifestation was an act of homage to the Stuarts, maybe as far back as the early 1680s. After 1745, when the first performance of God Save Our Noble King was recorded, the tune and multiple versions of the words became immensely popular. It eventually emerged as the British National Anthem - although no Act of Parliament or royal decree has ever been instituted to make it so. In fact the melody has been borrowed for use by some 20 countries or principalities in the course of the last 200 years, and is still the tune for Liechtenstein's national anthem. Among the contributors are the conductor Leonard Slatkin who tells how the tune was purloined by the USA for My Country 'Tis Of Thee - and Major Roger Swift at the Royal Military School of Music at Kneller Hall lets slip what The Queen feels about how the anthem should be performed"

Mick