Cllr Etheridge, who has led the group for three years, said he asked the council whether staff were working over the Easter break to “help process outstanding claims.”
However, this information, Cllr Etheridge said, was refused.
He said: “I’m not having the business sector treated like this and I feel gagged for asking one question.
“The Independents put in a formal complaint defending the private sector which was ignored and noted by the chief executive.”
Cllr Philippa Marsden, leader of the council and the Labour group, said: “The claims made by Cllr Etheridge that he has been ‘gagged’ or treated unfairly are completely untrue and inaccurate.
“To be frank, I do not have time for his political point scoring nonsense at the moment as my sole focus is to lead and co-ordinate the council’s response to the unprecedented coronavirus emergency.
“Unfortunately, it seems that not everyone recognises the significance of the current situation and we’ve had to remind Cllr Etheridge that it is not helpful for him to be placing additional, non-priority workload on staff who are already under huge pressure responding to this outbreak.”
Responding to Cllr Marsden’s comments, Cllr Etheridge added: “My Independent group have always supported staff and I was the first to congratulate them.
“As for political point scoring, perhaps we should ask the business sector their views on on their daily suffering and worries.”
Cllr Graham Simmonds of the Cefn Forest ward has taken over as leader.