Here's an item (dated 2000) about this, from radionewsweb about this:

April 17, 2000:In his radio column entitled "Jingle Fever" in the UK Sunday Times, Paul Donovan laments the marginalizing of one of the world's best known tunes.

It's not one of the many bits of extraneous sound which clutter up so much of the airwaves but " Lilliburlero" which has since 1943 been the signal for people the world over that BBC World Service News is about to begin.

Until recently it was played at the top of the hour but some two weeks ago new schedules reduced its use.

Not only that but the tune used now is not the one which would have been used during the second World War and which was also the official march tune for REME (Royal Electrical and Mechanical Engineers) during that war but a new arrangement with more strings and less brass.

Donovan comments that objections to the tune centred on its origin as a Protestant marching song some 300 years ago but that it now "stands more for utter trustworthiness than it does for sectarian hatred, and the BBC's decision to downgrade it is, at the very least, rather sad."