Elizaveta Berezovskaya told a coroner's inquest that her father said "something strange was happening to him" and said "some chemical reaction was inside him." The family later concluded he was suffering from depression.
Inquests are held in Britain to determine the facts in all cases of violent or unexplained death.
The body of 67-year-old Berezovsky a Kremlin insider turned critic of President Vladimir Putin was found on a bathroom floor of his ex-wife's home in southern England in March 2013.
Professor Bernd Brinkmann, an expert on hanging, told the inquest that he didn't believe Berezovsky had taken his own life, but had been strangled by someone who then made it look like a hanging.
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"In my view there is no way for death by hanging," he said, citing the marks on the dead man's neck and the coloring of his face as inconsistent with hanging deaths.
Pathologist Dr. Simon Poole said Berezovsky's injuries were consistent with hanging and there was no sign of struggle.
Poole said no defensive wounds were found, adding: "These injuries were extensively looked for."
Forensic scientist Sarah Tarrant said toxicology tests found traces of prescription medicines, including drugs for insomnia and depression. She said it was unlikely that any of them had contributed to Berezovsky's death.
A mathematician-turned-Mercedes dealer, Berezovsky amassed his wealth during Russia's chaotic privatization of state assets in the early 1990s. He later fell out with Putin and moved to Britain in 2001.