More than 1,200 people have responded to the current consultation on proposals for a new leisure centre and swimming pool at Elephant & Castle.
Local Liberal Democrat councillors have criticised the council's efforts to engage local residents in the consultation.
"We believe the consultation is desultory in the extreme," wrote Cllr Anood Al-Samerai in a letter to Cllr Fiona Colley, cabinet member for regeneration.
"The quality of the exhibition material was misleading and failed to give consultees the full range of options or the opportunity to fully explain their wishes.
"The online survey was similarly restrictive – reducing local people's long held ambitions to seven pitiful tick box options."
Cllr Al-Samerai also attacked the council's four-page wrap-around advertisement for the consultation in the Southwark News which did not mention swimming and stopped short of making a clear commitment to developing a new centre.
Last month two pupils from Crampton Primary School presented Cllr Colley with a 160-signature petition bearing the words: "We, the undersigned, believe that a large, good-quality swimming pool is an essential ingredient of the new leisure centre proposed for the Elephant & Castle."
"They turned the pool at Manor Place into a tip (literally)," says parent Miranda Newsom.
"The pool at the Elephant has been closed for years, with vague promises about 'when the regeneration happens…'
"We are forced to travel all the way to Peckham, Victoria or even the Latchmere Leisure Centre in Battersea when our children want to swim."
Cllr Fiona Colley has welcomed the responses received so far.
"The Labour administration has made it crystal clear that we are committed to building a new leisure centre and swimming pool at Elephant & Castle," she told the London SE1 website.
"We have already taken a clear decision on the site for the new centre and the current consultation is the next step towards making it a reality.
"Over 1,200 people have already responded to the consultation and I was delighted to receive a petition from children from Crampton Primary School in favour of a new swimming pool. Many other residents have emailed or written to me to give their views in more detail.
"The consultation deadline has been extended to this Friday 8 October to allow as many people as possible to have their say.
"Our next steps will be to analyse the responses and priorities of the local community and to start to draw up more detailed plans, as well as exploring further funding options in the hope of being able to afford a larger sports hall as well as the much needed swimming pool."