The Prime Minister confirmed on Tuesday that Britain would quit the single market when it exits the European Union, although she said she would back an "implementation" period.
The interventions by Barclays executives come after JP Morgan, HSBC and UBS all indicated Brexit would hit their London operations.
Financial-services companies, their taxes and jobs will go to competitor countries around the world rather than to European nations if London is frozen-out in negotiations, Khan said in an interview with Bloomberg Television's Francine Lacqua at the World Economic Forum in Davos Thursday.
Earlier this month, JP Morgan boss Jamie Dimon warned that up to 4,000 financial-sector jobs could be lost in Britain if it loses access to European financial markets.
German newspaper Handelsblatt reports that USA investment bank Goldman Sachs Group Inc (NYSE:GS) is planning to halve the number of employees it has in London.
'We're slowing down that decision'.
However, in a statement, the investment bank said: "We continue to work through all possible implications of the Brexit vote".
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'There remain numerous uncertainties as to what the Brexit negotiations will yield in terms of an operating framework for the banking industry.
But following her speech on Tuesday setting out her Brexit strategy, which includes a full departure from the European Union's single market, bankers have begun setting out their own exit plans - from London.
'As a result, we have not taken any decisions as to what our eventual response will be'.
UBS chairman Axel Weber said that about 1,000 of the Swiss bank's 5,000 employees in London could be affected by Brexit, while HSBC chief executive Stuart Gulliver said his bank will relocate staff responsible for generating around a fifth of its UK-based trading revenue to Paris.
Banks and financial companies in London have been waiting for some clarity on whether the United Kingdom will keep financial "passporting rights", which allow them to trade freely across Europe after it leaves the EU.
Jes Staley told the BBC: "I don't believe the financial centre of Europe will leave the City of London". "And of course the services that fit around the banks, asset management companies and insurance companies, are important to us as too".