NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Richard B. Langley
Date: 2024 Feb 17, 12:50 -0800
"If I remember correctly, the early morning forecast was preceded by a medley of sea tunes, but it's a long time since I was required to get up to listen to it, so I'm not sure if it's still there."
That was the Radio 4 UK Theme, which was played when Radio 4 switched back from the overnight BBC World Service relay to their own programming:
https://en.wikipedia.org/wiki/Radio_4_UK_Theme
It's long gone, unfortunately. You can find a version of it on YouTube but the original broadcast version running less than 5 minutes is hard to find. It used to be on a BBC website that has been archived and the link to it is now broken.
By the way, the pips were aired at 9:30 p.m. GMT on 5 February on Radio 4 to celebrate the 100th anniversary. It's very rare that they appears except on the hour. This was one of those occasions.