Flood Re was set up in June 2013 by the government in collaboration with the Association of British Insurers (ABI).
The ABI had said the scheme would be in place by summer 2015.
But Brendan McCafferty, from Flood Re, said it had "never commented publicly" on a launch date for the scheme - which still "needs to be tested thoroughly".
For much of the winter of 2013-2014, large parts of the Somerset Levels were underwater with dozens of homes flooded.
With flood-hit homeowners facing soaring insurance bills, Rebecca Horsington - from the Flooding on the Levels Action Group - said it was important to get the government scheme "in place as soon as possible".
"They've had 18 months to sort it out and now they're requesting a further year," she said.
"You don't want the scheme to fall at the first hurdle but you do have to question why it's taking so long.
"You can't have people ending up with no insurance."
But Mr McCafferty, CEO of Flood Re, said they were "working night and day" to get the scheme up and running as quickly as possible.
"Building a re-insurance company from a standing start is complicated," he said.
"It is a complex scheme which needs to be tested thoroughly if we are to get it right first time for UK home insurance customers."
Up to 500,000 homes will have their insurance capped under the plan, which is due to be launched in April 2016.
A Somerset action group says it is "disappointing" a scheme to make home insurance more affordable in flood-risk areas will not start until 2016.