Vadra submitted a medical certificate from Gangaram Hospital here informing a court here that a tumour in large intestine has been detected.
Vadra told Special Judge Arvind Kumar that his doctor has advised him to get a second opinion and therefore he wants to go to London to seek a second opinion.
Representing the ED, Solicitor General Tushar Mehta told the court that the doctor has not essentially asked Vadra to take a second opinion in London but only mentioned he can take it "if he wishes so."
He also said that the investigation in the case is at a crucial stage and there are chances Vadra may not return.
The ED also apprehended that Vadra might tamper with the evidence if he is allowed to go to London.
The ED also said there are treatment facilities available in India.
Countering the ED's submission, Vadra's counsel and Senior Advocate K.T.S. Tulsi said Vadra will not go to those places where the agency has objections.
The defence counsel said Vadra's medical condition can worsen with the passing of time.
Tulsi contended that it cannot be said that Vadra will flee the investigation.
Reserving the order on Vadra's plea, the court said it will decide on June 3 on his plea.
The case against Vadra relates to alleged ownership of overseas assets worth 1.9 million pounds. The charges against him pertain to undisclosed foreign assets and entities to evade tax.
Vadra was granted anticipatory bail on April 1 on the condition that he would not leave the country without permission and join the probe whenever required.
( With inputs from IANS )