Newham Council shelved leisure pool plans for the community post-Games due to spiralling costs and uncertainty about attracting sufficient private sector funding.
Newham and Tower Hamlets Councils had agreed to contribute a total of £7M towards the project's costs.
The total cost of the project was projected to be £40M.
Local authority chiefs are concerned that there is unlikely to be any cash available through section 106 agreements, as there are indications that these funds may be used to help fund projects including a new bridge or school in the Olympic Park after the Games have finished.
Andrew Boff AM said: "I’m disappointed that yet another positive benefit for local residents coming out of the Olympic Games looks likely to be shelved. This is a now common example of a complete lack of thought and forward budgeting by Olympics chiefs to deliver on the promise of long-term benefits for Londoners."
A spokesperson for the London Development Agency said: "The LDA and partners have carried out a feasibility study into leisure water uses such as wave machines and slides being added to the existing Aquatics Centre legacy plans. The two borough involved, Newham and Tower Hamlets, have decided not to pursue this option but they are working with the LDA through the legacy masterplanning process to ensure a sustainable plan for the area which will include both community and elite use after the Games. Any future proposal for leisure water use will continue to be evaluated throughout this process."