The vehicles were due to be housed in the new Gogar depot, which was originally set to be finished at the end of this year.
But work there has fallen badly behind and the Evening News can reveal that tram bosses are discussing sending the first four trams, currently being built in Spain, to the London borough instead.
Tram firm TIE insists the move is merely an opportunity to test the trams on a working network, but critics believe it is in fact because they have nowhere else to go.
Earlier this year TIE was forced to admit that work at Gogar was nine months behind schedule, although there are claims that work on the depot is actually running up to two years late.
John Carson, a former director of maintenance for Network Rail and long-standing opponent of the trams, said: "The depot is at least 18 months late, there's absolutely no doubt about that. They've nowhere to put them in Edinburgh, so Croydon is as good a place to hide them as anywhere else."
Shirley-Anne Somerville, an SNP MSP for the Lothians and an outspoken tram critic, said: "TIE have never even suggested that the trams would have to be tested out before being brought to Edinburgh.
"It's ironic that the only thing being delivered on time here are the tram themselves, with nowhere to store them and no track to run them on."
The final business case for the tram project, which was published in December 2007, scheduled the completion of the Gogar depot for the end of this year. However, tram bosses now say that timeline is out of date.
The first set of trams is expected to arrive in the UK in spring 2010, and discussions with Transport for London (TfL) are understood to have begun. A TfL spokesman said: "We offered our assistance to Edinburgh and are currently awaiting details of how they want us to help."
Alastair Richards, managing director of Edinburgh Trams, said: "We are currently exploring the possibility of testing a number of Edinburgh's trams on Croydon's network. It provides us with an excellent opportunity to get some miles under the belt and test the trams in a real environment.
"Coupled with the existing testing regime on test tracks and on new track in Edinburgh, this provides the Edinburgh tram with the best of both worlds and ensures that the vehicles will be the best that they can be when the scheme opens."
TIE chiefs have confirmed that they will take delivery of all 27 trams for lines 1a and 1b, despite the second route being dropped. The extra vehicles will ensure more regular services, they said.