Lord Lawson told the BBC: "The really important thing now is that we prepare for the no-deal outcome and it is grossly irresponsible if we don't prepare".
It follows claims Mr Hammond made this week to the Treasury select committee that he would not spend money preparing for a no-deal with the EU.
Amid reports of rancour between No 10 and the Treasury, the prime minister's official spokesman gave only a lukewarm endorsement of Hammond when asked about her views on Lawson's comments.
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Was it the added pressure of playing in Japan that did her in? Then the same thing happened at the Toray Pan Pacific Open. It might have been "a grudge match", her defeating Kerber in the Open and now Kerber overpowering her.
The call by Margaret Thatcher's long-serving chancellor comes amid growing concerns that Mr Hammond is trying to keep Britain in the European Union by the back door.
"He may not intend it, but in practice what he is doing is very close to sabotage", Lawson said. Spending money now on Brexit preparations would divert cash away from priorities such as the NHS and social care and the investment may turn out to be unnecessary if talks result in a good deal, he said.
However Lord Lawson said a no deal outcome was "the most likely outcome" of the talks so money should be spent now.
Michel Barnier said the the impasse was "disturbing" and said the European Union was not yet prepared to move onto talk about any future trade deal.
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