The first infant to be placed in the basket - which was already second-hand when her parents acquired it - was Christine Teal, from Stanningley in Leeds, who is now 65.
The wicker crib was originally a donation to her mum Emma Hart in 1953, when money was tight in post-war Britain.
It has since been passed between relatives living as far afield as Edinburgh and Portsmouth.
The cradle remains in perfect condition despite never being repaired or having had anything more than a wipe-down.
It has held 17 girls and 19 boys - including twin boys - and is now a bed for little Leeds baby Willow Abbiss, who was born in August this year and who is Christine's grandchild.
Christine's parents Ambrose and Emma moved from St Helen's, Merseyside, back to their home town of South Queensferry, near Edinburgh, after Ambrose had come out of the army.
Fitness instructor Christine said:
"I have an older brother and sister and I suppose my parents thought their family was complete, so when they moved back to Scotland they didn't take much.
"When my mum was pregnant with me she had to start from scratch so pretty much everything was donated.
"My mum then held on to everything and it was used for my two younger sisters, Dorothy and Pauline."
From there the Moses basket was used by the next generation, when it was handed to Christine's elder siblings, Keith and Florence, to be used for the six children they had between them.
By this time the basket had began its move to England after Christine met her Yorkshire-born husband while he was based in Scotland with the Royal Navy.
When he was posted to Portsmouth, Christine went to live with his family in Leeds.
It was then used for Christine's children, Julie and Jamie, and her two younger sisters' children.
Christine said: "At this point we weren't even thinking it was a family heirloom, it was just another pregnancy in the family and saying, 'oooh, we've got the Moses basket you can have'."
Before long the crib was being used by a third generation and the idea of it being a real family heirloom kicked in.
Christine said: "Before this we didn't even realise we had started a family tradition.
"But by the third generation of babies, it then became a requirement that any babies in our lineage had to be in the basket - it was a lovely thing we were doing.
"We have a little book now where each and every baby is detailed.
"We now make sure that every baby is photographed in the basket - before then we didn't bother with photos as much.
"Yes, we have pictures of each baby, but they're not always in the basket, you have to remember that babies are in the basket for a relatively short amount of time."
As the crib was being passed forwards and backwards to England - when Christine's sister Pauline also married into the Navy the basket started heading as far south as Portsmouth - each careful owner might add their own extra touch such as buying pretty bedding.
For that reason the crib has always stayed in immaculate condition.
"Nobody has ever painted it or broken it. We all treat the Moses with the upmost respect. It is now precious to us," said Christine.
"This has unintentionally become a family tradition originating from our mum.
"Mum and Dad both died over 20 years ago now, but I think my mum would be immensely proud of what we are doing.
"The basket has created a great bond and keeps us connected to each other, regardless of how far apart we are."
Only two of the babies in the family have not slept in the basket because they were born at the same time as other babies already in it.
The first fourth-generation baby was Quinn Simpson, who was born in October last year in Portsmouth. He is the great-great grandson of Keith, Christine's brother.
He would be the great-great-great grandson of original parents Emma and Ambrose.
The baby in the basket at the moment is Willow Abbiss, Christine's granddaughter, and lives in Leeds.
Glazier dad Paul Abbiss, 44, is Christine's son. His four daughters have all been in the basket.
Courtney Foster, born in 1995, was from a previous relationship.
Autumn, eight, Poppy, four, and Willow, two months, are all from his marriage to Leanne Abbiss.
Hairdresser Leanne, 36, said: "At first I thought it a little odd when I was told I had to have an old family heirloom for the girls, but it is actually really lovely.
"I feel honoured to be able to pass on this wonderful family tradition and it is a lovely way for us all to be connected to each other, to know that we are all part of this family and that we are all included.
"The way that this tradition is going I'm thinking the basket will still be in the family to be used by our daughters."