In December, Sir Ed warned that nearly 10 million people could see their democratic right to vote “ripped away” if some local elections in England were delayed.
But on Wednesday, a Lib Dem spokesperson said there were “specific circumstances in Cheltenham”.
“The councillors there have only been in place for 18 months as they had full council elections in 2024.
“That’s very different to Conservative councils like Essex, Hampshire and Sussex which last had elections in 2021, meaning their councillors will have served seven-year terms before facing re-election,” the spokesperson added.
In December, Reform UK Head of Policy Zia Yusuf told the BBC his party would try to secure a parliamentary vote to protest against such delays, which he called “extremely dangerous”.
The Conservatives have accused the government of being “scared of the voters”, but their leader, Kemi Badenoch, has indicated she will not stop Tory-led councils requesting a postponement.
Last February, the government said nine areas could postpone their 2025 elections until this year to help them prepare for the restructuring.
Ministers later asked all 63 councils affected by the reorganisation if they required a delay to the elections due this year.
In a statement released just before Parliament’s Christmas recess, external, Local Government Minister Alison McGovern said “multiple councils” had requested a postponement.