The proposed building designed by Faulkner Browns will replace the 34-year old Lee Valley Ice Centre with two Olympic size rinks.
If given the green light by Walthamstow borough council, the centre would be the first twin-pad venue in the south of England, and would also feature a new gym and exercise studio.
Work is expected to start by spring 2021.
Lee Valley Regional Park Authority is promoting the scheme, which will be built in two phases to maintain an open ice rink at the site at all times during construction.
The proposed building will have an 80,000 sq ft footprint and rise 10.5m in height.