Theresa May’s insistence that a Brexit trade deal with the EU must be reached within two years is already causing unnecessary damage to the economy by compounding uncertainty for businesses, the mayor of London, Sadiq Khan, has warned.

In response to No 10’s Brexit plan, the mayor on Monday called on the prime minister to prioritise striking an interim deal with the EU that would secure access to the single market and avoid a “cliff-edge” for British businesses.

He applied further pressure on May to heed warnings coming from businesses and the City of London on the same day Nicola Sturgeon, the Scottish first minister, said she would push for a second independence referendum.

No 10 has made clear it believes a trade deal with the EU can be struck in parallel with divorce talks over the next two years.

Ministers have stressed they are prepared to leave the EU with no trade deal at all, falling back on World Trade Organisation’s tariffs, if Brussels is not prepared to strike fair new trading arrangements.

However, Khan questioned May’s claim that no EU trade deal is better than a bad deal, saying it fundamentally underestimates the “colossal damage” that having no deal would cause.

He said the government’s lack of interest in striking an interim trade deal was a mistake and already causing difficulties for businesses, which are not feeling reassured about the plan.

“I believe that the government’s unrealistic expectation of having trade negotiations concluded within two years of triggering article 50 – with no plan for extending this period – is compounding uncertainty and risks, causing unnecessary damage to our economy,” Khan said.

“Many experts, including the former EU ambassador Sir Ivan Rogers, believe that concluding the negotiations within this time frame is impossible. If neither an interim or final deal is in place at the end of the two years the government has allowed then the UK would crash out of Europe and we would suffer very significant economic detriment.”

David Davis, the Brexit secretary, has only said he is prepared for implementation of the UK’s deal to be phased.

Khan highlighted the number of businesses already making preparations for downsizing in London out of fear about a harsh Brexit in two years’ time.

“There is growing concern in the business community about the unnecessary uncertainty caused by a real lack of clarity on the government’s negotiating position,” he said. “Some businesses including HSBC, UBS and JP Morgan are already beginning to move small numbers of staff from London to other European and world cities, and many more have announced contingency plans to do so over the coming months.”

He said May should prioritise an interim arrangement that replicates the market access provided by the European Economic Area in order to provide the medium-term certainty that businesses require.

Without a trade deal, and with the threat of companies leaving, Khan said it would be a disastrous course for the government to conclude that the best way forward for the UK is to reshape its economy as a “low-tax, low regulation, tax-haven”.

“London and Britain’s global competitiveness and influence in the world have been built on our nation’s historic openness, rich culture, progressive values and flair for innovation,” he said.

“Starting a race to the bottom would inevitably bring about a decline in our country’s prosperity and world standing.”