The court ruled that he was sane at the time of the murder, and it was extremely pre-meditated. And incited by all the far right material he had been reading.
Mental illness doesn't comprehensively eliminate culpability. The mental illness would have to explain why the act wasn't murder. Such as: the defendant was unable to foresee the act would cause death; the defendant believed they were acting in self defence.
In this case someone with a history of mental illness still premeditated to commit a political assassination.
He murdered her for a reason: he was a violent racist. His defense never maintained that he was insane and a judge determined that it was an ideologically-motivated murder.
"He had searched the internet for information about the British National Party, apartheid, the Ku Klux Klan, prominent Jewish people, matricide,white supremacism, Nazism, Waffen SS, Israel, public shootings, serial killers, William Hague, Ian Gow (another assassinated MP), and Norwegian far-right terrorist Anders Behring Breivik (about whose case he collected newspaper clippings)."
He also happened to be mentally ill, but that hardly seems relevant. Suppose Hitler was bipolar (he wasn't, but suppose he was), that would hardly be exculpatory.