The debate became heated over the confirmation of Labour Icknield councillor Asif Masood as understudy to town mayor Labour Leagrave councillor Sameera Saleem.
Councillor Masood was one of three Labour councillors seen to be socialising at a local gathering in breach of Covid-19 lockdown rules, nearly two years ago.
The three apologised unreservedly after photos emerged on social media triggering more than 100 complaints, with then-mayor Tahir Malik later resigning.
Liberal Democrat group leader and Barnfield councillor David Franks said: “Only 18 months ago, councillor Asif Masood was found guilty by the standards committee of bringing the council and his office into disrepute.
“This was through attending a garden party with other people at a time when such events were banned and Luton residents were falling ill from Covid by a dozen at a time.
“It would be interesting for someone to explain why all of a sudden he’s squeaky clean and can now be deputy mayor of the town.”
Labour Challney councillor Tom Shaw replied: “Of all the occasions the Liberals could raise this, they wait to the maximum publicity time at this annual meeting council.
“Let’s have a look at the case. They got caught. They apologised for it. The mayor resigned. In July 2020, the council’s fully apologised for it.
“You just want to play cheap political games. You’ve sunk as low as you possibly have tonight. You should be totally ashamed of yourself.
“The standards board had no power to impose sanctions on them. It asked them to give voluntary contributions to charity, which they all did.”
Liberal Democrat Wigmore councillor Peter Chapman warned: “Councillor Shaw, you’ve really gone too far tonight. I’ve been on this council 40 years and never once voted against a mayor or deputy mayor.
“We didn’t know until we were notified this afternoon who would be the candidate for deputy mayor.
“I believe to represent people on this council of Luton is one of the highest honours a Lutonian or someone who comes to live in Luton can have.
“I really can’t believe such moral values and shame aren’t part of this council now. Many people in Luton during the Covid pandemic went through hell.
“We’re now putting a councillor into deputy mayor who since bringing this council into disrepute has not put themselves before the electorate, so they can decide.
“My parents died during the Covid period in the same week. My mum died in hospital with Covid and we were unable to visit. It wasn’t a social event,” he added. “We couldn’t go.
“And you say I’m playing political games. It’s an utter disgrace. I’m furious you should say that, Tom.
“It’s a principle that if someone brings this council into disrepute, if they’re going to take a senior position with this council they should put themselves in front of the electorate before we give that privilege.
“I’m not playing political games. It’s my profoundly held view it’s wrong. I don’t expect to be criticised for having that view.”