Christian missionaries in El Salvador have been reunited with their baby after it was swapped at birth.

The British father, Richard Cushworth, and his Salvadorian wife, Mercedes Casanellas, accused a doctor at a hospital of swapping their newborn son as part of a child trafficking plot.

The missionary couple announced their joyful reunion on Facebook this morning.

"There are no words to express what our heart feels to have our baby at home! Thanks to all who joined our pain and fed our hope.

"Thank God our family has gathered, for the moment we are not allowed to upload photos but soon we'll give more details of the outcome of this miracle."

The Cushworths had accused Dr Alejandro Guidos, a gynaecologist present at the birth, of masteminding a plot to swap their lighter-skinned son with a darker-skinned baby in order to sell him to human traffickers.

Dr Guidos, who is under ongoing investigation, denied the charges.

"I'm perfectly calm," he said. "I have nothing to prove. I am innocent."

The Cushworths' biological son had been raised for three months by another couple, who had no idea they were raising the wrong child.

The babies of the two couples appear to have been mixed up by accident, Prosecutor General Luis Martinez said.

The Cushworths' family lawyer backed up this analysis and said the case "apparently" seemed to be an accidental mix up of the infants. He urged the hospital to review procedures to ensure it didn't happen again.

"We're all absolutely thrilled," Cushworth's father, David Cushworth, told the MailOnline. "This is an answer to so many prayers.

"All the circumstantial evidence pointed to a criminal act, but the official story we are being told appears to show it was a mistake, a mix-up.

"I feel for the other family. We know nothing about them, except that they only just found out today that their baby isn't really theirs. It must have been devastating."