Downing Street has said Theresa May has full confidence in Philip Hammond, amid calls for the Chancellor to be dismissed over an apparent lack of preparation for a “no deal” Brexit.

It comes after Lord Lawson, the former Conservative Chancellor, said Mr Hammond should be sacked for coming “very close to sabotage” for refusing to set aside millions to prepare for an exit from the EU without a deal.

But in a Westminster briefing, a spokeswoman for the Prime Minister said the two had a “very good working relationship”. Asked if Ms May has full confidence in the Chancellor, the spokeswoman replied: “Yes.”

Earlier this week, a rift opened up between Ms May and the Chancellor after Mr Hammond warned diverting funds in the current climate would mean less money for the NHS and social care – insisting funds would not be set aside until the “very last moment”, if the need became clear and negotiations with Brussels collapsed.

But in the Commons chamber at Prime Minister’s Questions, Ms May said she would spend taxpayers’ money immediately, telling MPs: “We are committing money to prepare for Brexit, including a ‘no deal’ scenario.”

Asked about the Chancellor’s comments, Lord Lawson (a prominent Leave campaigner during the EU referendum), said: “He may not intend it, but in practice what he is doing is very close to sabotage.”

He continued: “You have to spend money from time to time, and there is nothing more important than preparing for what has always been the most likely outcome.”

Lord Lawson also suggested a suitable replacement for Mr Hammond could be Michael Gove, who Ms May brought back to the Cabinet after June’s inconclusive election result.

The Sun newspaper also quoted one Cabinet source as saying that relations between the two had become so difficult that they “can't bear to be alone together in a room”.

Brexit: the deciders Show all 8 1 /8 Brexit: the deciders Brexit: the deciders European Union's chief Brexit negotiator, Michel Barnier Getty Brexit: the deciders French President Emmanuel Macron Getty Brexit: the deciders German Chancellor Angela Merkel Reuters Brexit: the deciders Commission President Jean-Claude Juncker EPA Brexit: the deciders The European Parliament's chief Brexit negotiator Guy Verhofstadt Getty Brexit: the deciders Britain's Prime Minister Theresa May Getty Images Brexit: the deciders Britain's Chancellor of the Exchequer, Philip Hammond PA Brexit: the deciders After the first and second appointed Brexit secretaries resigned (David Davis and Dominic Raab respectively), Stephen Barclay is currently heading up the position PA

Speculation regarding frustrations between Downing Street and the Treasury has been rife since Ms May refused to confirm that the Chancellor would continue in his role when asked in May – before the general election.

It was widely reported that the Prime Minister had intended to sack Mr Hammond, but lacked the political authority after losing the Conservative majority at the election.