Diedrick, 38, was arrested in 1995, but released without charge. The Crown Prosecution Service later decided that there was not enough evidence to prosecute.
Yesterday there were gasps from Dr Francisco's mother, Venus, and sisters Celia and Margrette as Mr Justice Alliott found for the family. Diedrick, from Maida Hill, west London, was not in court and did not give evidence.
It is thought to be the first civil action against someone when there has been no criminal prosecution connected to a murder. The family is seeking pounds 50,000 compensation for alleged assault and battery. The damages will be decided at a private hearing.
Margrette Francisco said the CPS would be "strongly urged" to charge Diedrick. The family's solicitor, Taz Raza, said that if it did not act and bring charges, a judicial review to challenge that decision would be sought.
Mr Justice Alliott said the family had established certain facts, including that Diedrick was obsessed by Dr Francisco and stalked her. He was desperate to speak to her, as he believed she was about to leave for the US for good or for a long time and that he had demonstrated violence in the past when faced with a comparable situation.
Diedrick had no alibi for the relevant period on the day of the murder. "I consider that those factors make out a very strong prima facie case. Therefore I have no hesitation in drawing an adverse inference from the defendant's failure to give evidence.
"If the defendant did not kill the deceased, I deem it incredible he would not seize the opportunity to declare his innocence rather than shelter behind a perceived tactical advantage."
The judge said Diedrick probably had no premeditated intent to kill. "But I am satisfied he first struck and then strangled the deceased by hand and ligature.
"This is a dreadful judgment to have to pass on any man ... but I find the assault and battery alleged, in effect the murder, to have been proved."
Margrette Francisco said that after a very long and difficult struggle her family felt that "the road to justice has finally been opened to us".
Fatal attraction, page 7Reuse content