And though the numbers have steadily dwindled, friends who attend the club this week hosted a party to celebrate the milestone.
Members as old as 98 joined in with ballroom, sequence, jive and Latin American dancing during the annual birthday event.
Organiser Brenda Booth, 77, was at the very first Morley Tea Dance and has been attending since.
She said: “It’s a long time is 35 years. Somebody once said that they thought we were the longest-running tea dance in the area, West Yorkshire.”
Alan Olbison, who at the time was a disc jockey at Pudsey Civic Hall events, set up the Morley dance, she said.
Mrs Booth, who was then in her 40s, was invited along with friends.
“[What I remember] is how many people were there, some in couples, some on their own.
“It was a good way to get people out and exercising and enjoying themselves.”
The dance came to be so crucial to Mrs Booth’s week that her former job as a lollipop lady, serving Birkenshaw Middle School, had to make way for it.
“I said, ‘I go somewhere really important on a Tuesday afternoon’,” and she did not work on that day of the week.
As the years have gone by, some things have changed.
In its heydey, more than 100 people could turn out to dances, which take place in Morley Town Hall, whereas now the average is around 60.
Mrs Booth, of Birkenshaw, said: “People are dying off and the youngsters don’t seem to want to do it now.”
She added: “Sometimes we do have a queue dance, where the ladies stand in front of the stage, the gents come and take the first lady, do once round the floor with them, drop them off and then come and get another lady, so everybody gets with a fellow, because a lot of people are widows.”
Despite the declining numbers, there are members who have been going for 20 years, and Mrs Booth said some had met their partners at the dances.
But other parts of the dance have changed too.
“We used to have proper refreshment people, which the council paid for. They did apple pies and all sorts, it was great,” said Mrs Booth.
Catering was later provided by Morley Elderly Action, but the members now take it upon themselves – enjoying tea, coffee and lemonade for 10p a cup – and if they wash up after themselves they get a biscuit too.
Stuart Jenner is now the DJ playing old favourites for the group.
Regular dancer Eric Castle, 98, is “still going strong” and also attends dances in Armley.
Mrs Booth said: “When Eric first came, I was on the door and he said, ‘Do you let 19-year-olds in?’ And I said ‘You look a bit older than that’. He said, ‘I am, I’m 91’.”
She thought he looked younger than that – but sure enough, Mr Castle brought his passport along the next week to confirm his birth was in 1920.
“If you do a quickstep with him, you know you’ve done it,” said Mrs Booth. “It goes fast.”