* Khan, business groups say transition deal is urgent
* Transition will be agreed as part of wider deal, UK says (Adds May comments in parliament)
LONDON, Oct 23 (Reuters) - London Mayor Sadiq Khan joined Britain's business leaders in warning that companies would start moving jobs and investment out of the country if they do not get a Brexit transition deal soon.
The boss of Goldman Sachs tweeted last week that he was looking forward to spending more time in Frankfurt after Brexit, and Britain's five leading business organisations warned on Monday that the threat to the economy was becoming critical.
"Just left Frankfurt. Great meetings, great weather, really enjoyed it. Good, because I'll be spending a lot more time there. #Brexit," CEO Lloyd Blankfein tweeted last Thursday.
With tensions mounting, the five employee groups have drawn up a letter to Brexit minister David Davis, warning that time was running out for companies which need to make investment decisions at the beginning of next year.
Prime Minister Theresa May has promised to retain full access to the EU's single market for two years after Brexit to limit the disruption for companies who do not know how they will trade with their neighbours in the future.
However, her spokesman said on Monday the government's position had always been that a transition deal would be finalised at the same time as the country agrees a new trade deal.
That prompted some lawmakers to ask how long companies would need to wait before they see the shape of the transition deal.
"We're looking to finalise a deal all in one go," the spokesman said. "The point is, of an implementation period, as the prime minister has set out, it's a bridge to where you're heading. You need to know where you're heading."
Asked to clarify her position, May told parliament: "An implementation period is about a period which is adjusting to the future relationship. That's the basis on which I put it forward to the European Union, and that's the basis on which we'll be negotiating an agreement on it."
Mayor Khan, a member of the opposition Labour Party who campaigned to remain in the EU, said Blankfein's comment reflected a wider thinking in the business community and warned that others would follow suit if a transition deal was not quickly agreed with Brussels.
"He's articulating publicly what many CEOs and investors who love working in London have been saying privately, which is that unless they have certainty about what happens after March 29, 2019, they have got to make a plan B," he said.
"He's not bluffing. When I speak to businesses each day, they're not bluffing."
May has said she understands the pressures on businesses however leading Brexit campaigners have started to call on the prime minister to walk out of the talks if Brussels does not agree quickly to move on to discuss future trading relationship.
May won a brief respite on Friday when EU leaders signalled they were ready to move the negotiations forward in the coming months.
"Agreement (on a transition) is needed as soon as possible, as companies are preparing to make serious decisions at the start of 2018, which will have consequences for jobs and investment in the UK," the draft letter from the five groups says, according to a person familiar with the situation.
"And the details of any transitional arrangement matter: the economic relationship the UK and EU has during this time-limited period must match as close as possible the status quo."
The letter is due to be sent from Britain's five leading business groups, the CBI, the British Chambers of Commerce, the Institute of Directors, the Federation of Small Businesses and the manufacturing group, the EEF.
In a separate quarterly survey from the CBI, optimism about the business situation was shown to be at its weakest since just after last year's Brexit vote. (Additional reporting by William James; Editing by Robin Pomeroy)