Lord Justice Burnett and Mr Justice Irwin rejected the appeal from Christian pro-life campaigner Aisling Hubert who was seeking a judicial review of the Crown Prosecution Service's (CPS) decision not to press charges.
Dr Palaniappan Rajmohan and Dr Prabha Sivaraman were secretly filmed by the Daily Telegraph allegedly agreeing to abort a baby because she was a girl.
The Crown Prosecution Service (CPS), then led by Mr Starmer, decided not to prosecute even though it admitted there was enough evidence to get a conviction.
Ms Hubert attempted to bring a private prosecution earlier this year against the doctors but the CPS blocked this, again in the "public interest".
But Mr Justice Irwin said there was never going to be an abortion and the only evidence concerned 'preparatory acts'.
The judges are to set out their full reasons at a later date.