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Under the Political Parties, Elections and Referendums Act 2000 the Electoral Commission is responsible for the conduct of referendums, including estimation of the costs. The Department has made no detailed estimate of the costs of a national referendum.
As a guide, we might expect the cost of running a UK-wide referendum to be similar to the cost of a general election. The general election in 2005 cost in excess of £80 million.
In addition to the costs of conducting a referendum, the Electoral Commission would incur its own additional costs. These costs would be reflected in the Electoral Commission's estimate of its income and expenditure, which it is required to submit to Speaker's Committee annually. If approved, the money comes directly from HM Treasury to the Commission.
I understand that the Commission currently estimates that these costs would depend on the level of public information activity required, but would likely be in the range of £10 million to £30 million.