Complex sentence: The BBC made several compilation programmes and "best of" editions in recent years and favoured "Bring Me Sunshine" as the most popular song they used which has made it more consciously associated with them than the other tunes.
Split into simpler sentences: The BBC made several compilation programmes and "best of" editions in recent years and favoured "Bring Me Sunshine" as the most popular song they used. As a result, it is more consciously associated with them than the other tunes.