David Cameron and Nick Clegg both poured cold-water on Michael Gove's plan to give the Queen a yacht to celebrate the diamond jubilee on Monday.

In a letter to cabinet colleagues obtained by the Guardian, Michael Gove had suggested the government buy the Queen a yacht to celebrate the royal jubilee - at an estimated cost of £60m.

Gove said the Royals should be granted a new yacht - "in spite, and perhaps because of the austere times" - as a way of lifting the nation's spirits.

"My suggestion would be a gift from the nation to her majesty; thinking about David Willetts's excellent suggestion of a royal yacht, and something tangible to commemorate this momentous occasion."

Speaking to journalists after a speech on the economy, the deputy prime minister joked it was a case of "the haves and the have yachts" .

But he said although the diamond jubilee was a "wonderful occasion" he was unsure if it was a good use of public money. "I suspect most people in the country would think, given that there’s very little money around, that this probably wouldn’t be top of their list of priorities for the use of scarce public resources."

Later on Monday morning a Number 10 spokesman said David Cameron believed it would not be "appropriate" to spend public money on a new boat for the Monarchy.

Speaking in the Commons on Monday afternoon Gove insisted that while he supported the idea of a yacht he was not suggesting public funding should be provided for one.

The royal yacht Britannia, which served the Queen for 44 years, was decommissioned by the Labour government in 1997.

Labour Party deputy chairman Tom Watson said Gove was "out of touch" at a time of spending cuts. "We're all looking forward to the diamond jubilee. The significance of the occasion should be celebrated across the country," he said.

"When school budgets are being slashed, parents will be wondering how Gove came even to suggest this idea. This is not the time to spend £60 million on a yacht."

The subject of the yacht was raised in the Commons last year when MPs debated the budget for the Monarchy. Tory MP and staunch royalist Jacob Rees-Mogg asked: "Is there any chance that for the diamond jubilee we will get the yacht back?"

While Edward Leigh, the former chairman of the public accounts committee that scrutinises public spending said "stingy" Labour's decision to scrap the Britannia was a "tragedy".