Litter and rubbish continues to blight the Oasis Leisure Centre site, as details of its long-term future remain unknown.
The building was given Grade II-listed status last December after a year-long campaign to save it.
It came after landlord Seven Capital revealed plans to rebuild and reopen it as a leisure centre. But they inolved removing the dome and lagoon pool that attracted visitors to Swindon for 44 years.
During public question time at Swindon Borough Council's full meeting, member of the public Josie Lewis told leader David Renard legal action was possible, due to what campaigners described as "neglect and obvious reluctance" to keep it in good order.
She said there w numerous numerous complaints from the public because the Oasis has been continually blighted with litter for months on end.
They were "sick of the eyesore that blights The Oasis site."
Coun Renard said SevenCapital recognised "that under the terms of their lease they are responsible for the Oasis".
He explained: "They have been delayed in working up their proposals to refurbish and bring the building back in to use by having to await the outcome of the listing process, and now having to factor in the dome has been listed.
"The site is difficult to secure and it is unfortunate that whilst plans are being worked up, it suffers from regular instances of litter and rubbish being dumped due to unauthorised access to the site."
He added that SevenCapital endeavoured to keep the site clean and tidy but at times, due to the amount of litter and rubbish left, the site can be untidy.
He assured Ms Lewis the council’s focus in working with SevenCapital was on how the Oasis could be refurbished and brought back into use, but recognised this was more challenging to deliver as a result of the dome being listed.
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