If you don't know the tune - and whether you play in a band or not - may I recommend it to you?
The great cornet-player Shaye Cohn (though barely visible in the video) was this time playing piano, with Barnabus Jones on trombone. Michael Magro was on clarinet and Ben Polcer on trumpet.
I found that the tune was written by Carmen Lombardo in 1945.
I also found from other performances by singers on YouTube that it has touching words - about a couple who have been in love for many years and whose love is just as strong as ever.
So, all in all, a great song and one I am very pleased to have come across.
I spent time on my keyboard, trying to play along with the video. I soon noticed that - in terms of chord progression - it comes in the 'Salty Dog' category. That is to say it begins with four bars based on the chord of the sixth note of the scale and these are followed by four bars based on the chord of the second note of the scale.
There is no middle eight: it has one of those 16 + 16 structures, easy to memorise.
Finally, as I usually do, I wrote up my attempt at Seems Like Old Times in my mini filofax, so that I can have this as a future aide-mémoire. Although Loose Marbles was playing it in the Key of F, I put it in G as that is more convenient to me as a Bb cornet player.