HMT are going to be working hard over the next few weeks ... they say they're up to 18,000 suggestions for the Spending Challenge.
Whilst reluctant to suggest a Downing Street Petitions type site (much as I loved it), fearing too many votes for "Abolish tax", "Pay Ministers Nothing" or "Scrap the Department of X" ... But ...
This kind of idea volume could be dealt with through the over-used crowd sourcing with the best couple of hundred ideas being worked up by whoever wants to work on them, aided by government insiders (who would know the data that would be needed), leading to ideas that were implementation-ready far sooner than they might otherwise be. And, perhaps, a ready and able gang of volunteers who could help manage and monitor them through the delivery process.
Anyway, I submitted that idea under the label of "not really a cost save ..."