Digital ID plans backed by Sir Tony Blair will go ahead despite the Government admitting it does not know how much it would cost. When challenged on the tab facing British taxpayers, Darren Jones, the Chief Secretary to the Prime Minister, said “as of today we do not know the answer” but stressed he would be “coming back” with the figures after a consultation.

Sir Gavin Williamson, a Conservative MP, called it “utter madness” for the Government to start a project of such scale “without the slightest idea of what the cost will be”. He added: “You cannot claim that you will deliver savings when you do not know what the initial cost will be. This is a bad idea that not only infringes people’s civil liberties but will end up costing billions of pounds.”

Ministers have launched an eight-week consultation on the system known as the BritCard to ask the public how the “government by app” scheme should work.

But the launch was mired in drama, with Cabinet members reportedly refusing to support the rollout. It was reported that both Wes Streeting, the Health Secretary, and Bridget Phillipson, the Education Secretary, had told colleagues their departments would not hand data over.

A BritCard scheme has previously been touted as a way to curb illegal immigration, with the requirement to have one said to make it harder for people to work in the so-called black economy.

But ministers have moved away from making digital ID mandatory for workers and are now promoting it as a way to make it easier for parents to access services for their children.

Mr Jones said he wanted to “make public services work for you”, saying that the ID scheme would “make that possible, allowing you to log on and prove who you are to access public services more quickly, easily and securely”.

Yet critics lampooned the scheme, with Tory MP Mike Wood saying the Government had branded the rollout essential “for months”, adding: “It had to be mandatory, even for babies.”

He added: “But after months of insisting the scheme was indispensable, the Government is now asking the public to tell them just what it is indispensable for.

“There was a time when this was supposed to be the magic bullet to tackle illegal migration. Now the Cabinet Office seems to be suggesting it might just help reduce hold time on government call centres.”

Supporters of the scheme point to Estonia, where 99% of the country signed up to its digital ID scheme. It is reported to save the country billions of euros a year.

The Government announcement of the scheme last year hailed the Indian system, which has saved $10billion (£7.3million) annually.

Former prime minister Sir Tony Blair has supported the scheme, which his think tank described as a “landmark moment”.

He introduced ID cards in 2006, which were briefly rolled out in Manchester three years later before being abolished by the Coalition Government.