[720p/50 re-upload] BBC1 | closedown | 1st March 1983 (I think???) 

© BBC TELEVISION 1983
The sound and picture on this clip gets significantly worse during the closing announcement. The edge of the tape carrying the sound and control tracks was damaged as this was right at the end of a mould-covered, shite, cheap-ass Currys-branded Beta tape that had rolls of tape sticking together. I could hear them getting unstuck as the tape played through! In the original upload it took several attempts for my venerable 1982 Sanyo VTC5000 to play the tape without a rolling picture!
In the absence of concrete proof from BBC Genome (as Radio Times many weeks in 1983 just carried the Phil Silvers Show/Sgt. Bilko name with no episode titles or descriptions), I used Genome to match up the unbilled Sgt. Bilko episodes that ended at approx 00:10am between 1983 (as Breakfast Time is mentioned by the announcer) and 1985 (when this BBC1 branding ceased to be used). There were none in 1984 or 85 that were shown this late. So that left 1983. The only billing I could find on Genome for an un-named episode in 83 with a time of year's weather that could still (just) conceivably have overnight temperatures as low as -2 to -4 Celsius was 1st March 1983. I'd love it if someone who is reliable with dating these things could confirm or deny if I'm right.
For the announcer’s shift tonight, they’ve dug out Colin Ward-Lewis.
End of Sgt. Bilko/Phil Silvers Show and the Colonel's Secretary
BBC1 virtual globe: Weather forecast with Jim Bacon
BBC1 clock (00:13am): closing announcement
BBC1 mirror globe with national anthem
Black and silence
Black and tone (tape runs out)