The government sets out its agenda for the next parliament in the Queens Speech, which is really nothing more than a grandiose rubber stamp, all pomp and ceremony. This wouldn't be necessary in the Interactive Democracy system because each new Bill would be driven by voter demand: voters would set the agenda, not the politicians. ID is different to the Swiss system of Direct Democracy which allows the government to play its own tune unless a petition greater than 50000 voters demands change.
You may assume that ID subverts the role of the Queen, but that's not the whole picture. The royals can continue to have a role under ID, much as they do today. They may even expand their remit and initiate their own petitions for change, being well positioned to garner public support.