Nicola Sturgeon has hit out at Theresa May after the Prime Minister ruled out a ‘soft’ Brexit and signalled that Scottish ministers would be frozen out of decisions around the terms of the UK's departure from the European Union.

Mrs May vowed that any deal would have to include controls on the numbers of people coming to Britain.

The move makes it increasingly likely that the UK will have to leave the Single Market.

She also made clear that the Conservative Government alone would decide the terms of the UK’s exit and when to begin negotiations with Brussels.

Mrs May flew to Edinburgh for talks with Ms Sturgeon within days entering Downing Street earlier this year

There she told the First Minister she would not trigger the formal process for leaving the EU until she had agreed a "UK approach" and that she was "willing to listen to options" on Scotland's future relationship with the EU.

The SNP leader has also warned that limits on EU migration would be disastrous for Scotland's attempts to grow its population.

A spokesman for Ms Sturgeon said that the Conservative Government was in an “increasingly unacceptable and irresponsible position” on Brexit.

He added that Mrs May had given a “very clear undertaking when they met recently that she is prepared to consider options that the Scottish Government puts forward to protect Scotland's interests”.

Emily Thornberry, the shadow Foreign Secretary, accused the Conservative Government of “sheer high-handed arrogance for (saying) they will take all the decisions themselves”.

Ms Thornberry said that negotiations should be put on ice until ministers produced clear proposals about what they wanted to achieve.

The devolved administrations, opposition parties, MPs and the public should then get a chance to approve the plan, she said.

A spokesman for the Prime Minister said that the cabinet was committed to ensuring that Brexit works for Scots.

"But Cabinet members were clear that it is the United Kingdom's Government's decision to establish its terms and on when to trigger Article 50 (and begin negotiations)."

A No 10 source said that the Scottish Government would “feed” into discussions, but that decisions would be taken by the UK Government.

The cabinet also agreed that it would seek a “unique" model and "not an off the shelf solution".

This "must" include controls on the number of people coming to the UK from Europe "but also a positive outcome for those who wish to trade goods and services.”

This effectively rule out the approach of the Norwegians, who offer free movement to EU migrants in exchange for access to the Single Market.

Earlier, the Conservative former business minister Anna Soubry warned Mrs May that UK companies “could not survive” a crackdown on EU migration.

Mrs May also told her cabinet there must be no attempt to stay in the EU “by the back door”.

Once negotiations with Brussels begin a deal has to be thrashed out within just two years.

The UK Government fears that it could hand other EU countries a critical advantage if it starts talks without a clear plan.

Some EU leaders have already suggested that the UK should get the worst possible deal from the EU, to discourage other potential breakaway states.

Chuka Umunna, the Labour MP and chair of Vote Leave Watch, said that any proposed Brexit deal would be measured against the promises of Leave campaigners currently in the cabinet.

"There is no sign of the £350 million extra a week they said they would spend on the NHS, they will still not commit to give EU citizens already living in Britain the right to stay, and they refuse to preserve EU rules which protect workers' rights," he said.

"The promises of Vote Leave ministers like Boris Johnson were clearly not worth the paper they were written on.”

Separately, it was announced that the Conservative party's membership has grown by almost 50,000 over the summer.

The theme for the party’s annual conference in October will be "a country that works for everyone".

But, given the Brexit result, the opening day will be devoted to the global economy and an attempt to show that the UK is still open for business.