Residents fear a pergola could pose safety issues for an upcoming community celebration.
The Friends of Islands Gardens group has contacted Tower Hamlets Borough Council about the structure, in Island Gardens Park.
Member Eric Pemberton said it appeared to be leaning to one side and is “out of true”, a situation which had worsened during the past three years.
It was installed around 15 years ago.
He called on the authority to take action and wrote: “As the Friends are forward planning for celebrations commemorating the 120th Anniversary of the opening of the gardens may we please be assured the structure is not likely to lean any more and cause injury or damage to visitors by collapsing or suddenly lurching to one side further?”
The group will mark the milestone on August 1, with events including a Punch and Judy show.
A council spokesperson said: “A council structural engineer has inspected the bandstand this morning.
“The inspection showed the structure maintained its original shape.
“There are no signs of buckling or movement within the columns and the structure is sound with a number of support points and columns to secure the structure.”