This is quite a confusing appearance - as this was a late night programme, not as many fans would have seen it at the time - the memories of those that did see it conflict in their recollections of what was shown. Until or unless it is re-shown or tracked down at the BBC, this one will probably remain something of a mystery.  But ever hopeful, I'll leave it here until we know otherwise.

Apparently some footage of ABBA being presented with the 1977 Carl Alan Award by Princess Margaret when they visited London in February 1978 was shown on Come Dancing. 

The Carl Alan Award was first presented in 1953 and honours people who have made a significant contribution to the dance and theatre industry, such as teachers, performers and choreographers (other notable winners have been Roy Castle, Bruce Forsyth, skaters Jayne Torvill and Christopher Dean, dancers Wayne Sleep and Darcey Bussell, ex-Strictly Come Dancing professionals Darren Bennett, Matthew Cutler, Lilia Kopylova and ex-Strictly Come Dancing judges Len Goodman and Arlene Phillips) - which would at least explain why the presentation was shown on Come Dancing (if indeed it was).

Various fan memories:

1. One ABBA on TV regular, Richard K, seems to remember that "the award was for best choreography in the Take A Chance On Me PROMO - and that a clip of the PROMO was shown. However, they probably only filmed the PROMO around that same time so the award for that was a bit premature .... On the same night they received the Carl Alan Award (again) from Princess Margaret. As I saw it on TV as it happened. By accident. It was at the Lyceum Ballroom in London - now the Lyceum Theatre, where The Lion King plays. "
   
   
2. However, in response to point 1 above, in January 2007, Carl Magnus Palm said, "I'm pretty certain this is incorrect, since the award was for achievements the previous year (ie. 1977). However, the information I DO have is somewhat contradictory. Some sources say they were awarded the Carl Alan Songwriting Award, which indicates that it was for their song writing (duh!) whereas other sources say that it was for being "the most popular group".  This is confusing because the Carl Alan Award is for dance rather than songwriting.
   
   
3. Richard remembers, "But something makes me think this - I remember watching  Come Dancing (as it was just on) and being totally surprised ABBA suddenly came up. Why it would be shown in late 1979 is also odd - unless it was a repeat."
   
   
4. However, another ABBA fan says, "I very much doubt the Carl Alan clip was shown on Come Dancing and definitely not at the dates shown. The 1978 series of Come Dancing (7 shows) ran from July to September. The 1979 series also ran during the summer, so the dates given are definitely wrong. There is no reference in the BBC archive to the clip being shown and, in this case, I would expect it to be mentioned as the award was presented by Princess Margaret. The Royals' appearances are incredibly well-documented, even the smallest clips as in this case. There are, however, still two possible Come Dancings: 9 Aug 1978 and 16 Aug 1978. There are no details for either programme in the archive, which, given the detailed notes for other episodes in the same series, suggests that they were wiped [which is possible as widespread wiping only stopped in 1978]."
   
   
5. July 2008: Terry Malloy says, "I remember watching the 1978 show and it WAS shown as a special Come Dancing episode! These awards were for "Best Record to Dance to by a Popular music Group", voted for by people in the ballroom dancing profession. ABBA won it in 1977 for Dancing Queen, then in 1978 for Take A Chance on Me . The 1978 episode was broadcast twice - once in about March, not long after ABBA's visit to UK, then repeated late summer, around the release of Summer Night City."  Terry's recollections appear to be confirmed in the UK ABBA Fan Club Newsletter from October 1978 which says, "Since the last newsletter in July ABBA have appeared twice on British TV, The Carl Allen Awards were repeated."
   
   
6. March 2017: Ian Shaw says, "I'm sure this award was something to do with composers or something like that and there was always a big band on Come Dancing! I am positive I watched it one night and ABBA were there in person to recieve it from Princess Margaret! ABBA tunes used to be played by the band quite regularly!"
   
   
7. March 2017: Ray Morrison says, "I definitely remember them coming on to a lateish evening tv show to get this award and I'm sure it was Come Dancing. My folks had it on and I was amazed ABBA just walked in to take the award!"

The photo of Princess Margaret posing with ABBA after presenting the award accompanied Princess Margaret's dress when it was displayed at Kensington Palace in 2016.

Thanks to "P", Charlie McNab, Carl Magnus Palm, Ken Griffin, Gill Daniel, Richard Knight and Richard Simcock c/o ABBAMAIL (no longer online) and Michael Price. Extra thanks to Terry Malloy.  Thanks to Ian Shaw, Ray Morrison and Bryan Anderson c/o ABBAtalk (Facebook group).