Help me prove she's right - find this video

My grandmother has had dementia for some time but she has moments of absolute lucidity. My mother, however, insists that things she says during those moments are rubbish. She's wrong. She has form for gaslighting in general but this is getting a bit much...

The last couple of times GM has been lucid, she's told me she remembers a video that I used to watch as a child (I was born in 87 so late 80s/v early 90s). It was a live action sort of thing with real (overly smiley) people singing songs - some nursery rhymes, but also some more current (for then) stuff. I remember this too but I cannot find the video or even its title - can anyone help?

Some of the songs I remember from the video with details:

The sun has got his hat on (one man and one woman singing this both with straw hats that had a hole in the top - when they put them over their face it looked like a smiley sun with the brim as the corona)

Lambeth walk

Boiled beef and carrots

This ole house - sung by a very smoky man next to a sort of cartoon/graphic of a house which kept losing parts

Getting to know you

Underneath the spreading chestnut tree - smiley man wore yellow for this one and kneeled down while some woman sat on his knee

It's a very long shot but I need to prove my poor GM right and get my toxic mother to back down. Anyone ever heard of this?